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  1. Home
  2. Books
  3. Proper and Improper Forcing
  • Cited by 6
Publisher:
Cambridge University Press
Online publication date:
April 2017
Print publication year:
2017
Online ISBN:
9781316717233
DOI:
https://doi.org/10.1017/9781316717233
Subjects:
Mathematics, Logic, Categories and Sets, Programming Languages and Applied Logic
Series:
Perspectives in Logic (5)
Information

Book description

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the fifth publication in the Perspectives in Logic series, studies set-theoretic independence results (independence from the usual set-theoretic ZFC axioms), in particular for problems on the continuum. The author gives a complete presentation of the theory of proper forcing and its relatives, starting from the beginning and avoiding the metamathematical considerations. No prior knowledge of forcing is required. The book will enable a researcher interested in an independence result of the appropriate kind to have much of the work done for them, thereby allowing them to quote general results.

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Contents

Contents
References
References
More References
Abraham, Uri. Lectures on proper forcing. In Foreman, M. Kanamori, A. and Magidor, M., editors, Handbook of Set Theory .
Abraham, Uri. Isomorphisms of Aronszajn trees and forcing with-out the generalized continuum hypothesis (in Hebrew). PhD thesis, The Hebrew University, Jerusalem, 1979.
Abraham, Uri and Shelah, Saharon. Forcing closed unbounded sets. The Journal of Symbolic Logic, 48:643–657, 1983.
Abraham, Uri and Shelah, Saharon. Isomorphism types of Aronszajn trees. Israel Journal of Mathematics , 50:75–113, 1985.
Abraham, Uri and Shelah, Saharon. A Δ 2 2 well-order of the reals and incompactness of L(QMM) . Annals of Pure and Applied Logic , 59:1–32, 1993.
Avraham, Uri (Abraham), Devlin, Keith J., and Shelah, Saharon. The consistency with CH of some consequences of Martin's axiom plus 2 N0 >N 1 . Israel Journal of Mathematics , 31:19–33, 1978.
Avraham, Uri (Abraham) and Shelah, Saharon. Martin's axiom does not imply that every two N 1-dense sets of reals are isomorphic. Israel Journal of Mathematics , 38:161–176, 1981.
Avraham, Uri (Abraham) and Shelah, Saharon. Forcing with stable posets. The Journal of Symbolic Logic , 47:37–42, 1982.
Balcar, Bohuslav, Pelant, Jan, and Simon, Petr. The space of ultrafilters on TV covered by nowhere dense sets. Fundamenta Mathematicae , CX:11–24, 1980.
Balcar, Bohuslav and Simon, Petr. Cardinal invariants in Boolean spaces. In Novak, J., editor, General Topology and its Relation to Modern Analysis and Algebra, Proceedings of the fifth Prague Topology Symposion 1981 , volume V, pages 39–47, Berlin, 1982. Helderman Verlag.
Bartoszyński, Tomek and Judah, Haim. Set Theory: On the Structure of the Real Line . Peters, A K, Wellesley, Massachusetts, 1995.
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Baumgartner, James E.. Results and independence proofs in combinatorial set theory . PhD thesis, Univ. of Calif. Berkeley, 1970.
Baumgartner, James E.. All N 1-dense sets of reals can be isomorphic. Fund. Math. , 79:101–106, 1973.
Baumgartner, James E.. A new class of order types. Annals of Math. Logic , 9:187–222, 1976.
Baumgartner, James E.. Almost disjoint sets, the dense set problem and partition calculus. Annals of Math Logic , 9:401–439, 1976.
Baumgartner, James E.. Almost disjoint sets, the dense set problem and partition calculus. Annals of Math Logic , 9:401–439, 1976.
Baumgartner, James E.. Iterated forcing. In Mathias, A., editor, Surveys in Set Theory , volume 87 of London Mathematical Society Lecture Notes , pages 1–59, Cambridge, Britain, 1978.
Baumgartner, James E.. Ultrafilters on ω . The Journal of Symbolic Logic , 60:624–639, 1995.
Baumgartner, James E., Harrington, Leo, and Kleinberg, Eugene M.. Adding a closed unbounded set. The Journal of Symbolic Logic , 41:481–487, 1976.
Baumgartner, James E. and Richard, Laver. Iterated perfect-set forcing. Annals of Mathematical Logic , 17:271–288, 1979.
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David, Shai Ben. On Shelah's compactness of cardinals. Israel J. of Math. , 31:34–56 and 394, 1978.
Blass, Andreas and Shelah, Saharon. There may be simple P N1-and P N2-points and the Rudin-Keisler ordering may be downward directed. Annals of Pure and Applied Logic , 33:213–243, 1987.
Burke, Max R. and Shelah, Saharon. Linear liftings for non complete probability space. Israel Journal of Mathematics , 79:289–296, 1992.
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Devlin, Keith J.. N 1 trees. Ann. Math. Logic , pages 267–330, 1978.
Devlin, Keith J.. Concerning the consistency of the Souslin Hypothesis with the continuum hypothesis. Ann. Math. Logic , 19:115–125, 1980.
Devlin, Keith J. and Johnsbraten, Havard. The Souslin problem , volume 405 of Lecture Notes in Mathematics Springer, Berlin, 1974.
Devlin, Keith J. and Shelah, Saharon. A weak version of ◊ which follows from 2 N0 < 2 N1 . Israel Journal of Mathematics , 29:239–247, 1978.
Devlin, Keith J. and Shelah, Saharon. A note on the normal Moore space conjecture. Canadian Journal of Mathematics . Journal Canadien de Mathematiques , 31:241–251, 1979.
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Džamonja, Mirna and Shelah, Saharon. ♣ does not imply the existence of a Suslin tree. Israel Journal of Mathematics (submitted).
Eklof, Paul C. and Huber, Martin. On the rank of Ext. Math. Zeitschrift , 174:159–185, 1980.
Eklof, Paul C. and Huber, Martin. On the p-ranks of Ext(A,G), assuming CH. In Abelian Group Theory , volume 874 of Lecture Notes in Math., pages 93–108. Springer, 1981. (Oberwolfach 1981).
Eklof, Paul C. and Mekler, Alan. Almost free modules; Set theoretic methods . North Holland Library, 1990.
Eklof, Paul C., Mekler, Alan H., and Shelah, Saharon. Uniformization and the diversity of Whitehead groups. Israel Journal of Mathematics , 80:301–321, 1992.
Eklof, Paul C., Mekler, Alan H., and Shelah, Saharon. Hereditarily separable groups and monochromatic uniformization. Israel Journal of Mathematics , 88:213–235, 1994.
Eklof, Paul C. and Shelah, Saharon. A Combinatorial Principle Equivalent to the Existence of Non-free Whitehead Groups. In Abelian group theory and related topics , volume 171 of Contemporary Mathematics , pages 79–98. American Mathematical Society, Providence, RI, 1994, edited by Goebel, R., Hill, P. and Liebert, W., Oberwolfach proceedings.
Engelking, Ryszard and Karlowicz, Monika. Some theorems of set theory and their topological consequences. Fundamenta Math. , 57:275–285, 1965.
Foreman, Matthew, Magidor, Menachem, and Shelah, Saharon. Martin's maximum, saturated ideals, and nonregular ultrafilters. I. Annals of Mathematics. Second Series , 127:1–47, 1988.
Foreman, Matthew, Magidor, Menachem, and Shelah, Saharon. Martin's maximum, saturated ideals and nonregular ultrafilters. II. Annals of Mathematics. Second Series , 127:521–545, 1988. Will reapeare (in a revised form) in chapter XIII of [Sh f].
Fremlin, David H. and Shelah, Saharon. Pointwise compact and stable sets of measurable functions. Journal of Symbolic Logic , 58:435–455, 1993.
Friedman, Harvey. One hundred and two problems in mathematical logic. J. of Symb. Logic , 40:113–124, 1975.
Fuchino, Sakaé, Shelah, Saharon, and Soukup, Lajos. Sticks and clubs, preprint.
Fuchs, Laszlo. Infinite Abelian Groups , volume I, II. Academic Press, New York, 1970, 1973.
Galvin, Fred, Jech, Thomas, and Magidor, Menachem. An ideal game. J. of Symb. Logic , 43:284–292, 1978.
Gitik, G.. The negation of SCH from O(κ) = κ ++ . Annals of Pure and Applied Logic , 43:209–234, 1989.
Gitik, Moti and Shelah, Saharon. Cardinal preserving ideals. Journal of Symbolic Logic (submitted).
Gitik, Moti and Shelah, Saharon. On the II-condition. Israel Journal of Mathematics , 48:148–158, 1984.
Goldstern, Martin. Tools for your forcing construction. In Set Theory of the Reals , volume 6 of Israel Mathematical Conference Proceedings , pages 305–360.
Gray, C.. Iterated Forcing from the Strategic Point of View . PhD thesis, UC Berkeley, 1982.
Grossberg, Rami and Shelah, Saharon. On the structure of Ext p (G,Z). Journal of Algebra , 121:117–128, 1989.
Hajnal, Andras. Proof of a conjecture of S.Ruziewicz. Fundamenta Mathematicae , 50:123–128, 1961.
Harrington, Leo and Shelah, Saharon. Some exact equiconsistency results in set theory. Notre Dame Journal of Formal Logic , 26:178–188, 1985. Proceedings of the 1980/1 Jerusalem Model Theory year.
Hart, Bradd, Laflamme, Claude, and Shelah, Saharon. Models with second order properties, V: A General principle. Annals of Pure and Applied Logic , 64:169–194, 1993.
Hiller, Howard L., Huber, Martin, and Shelah, Saharon. The structure of Ext(A, Z) and V = L . Mathematische Zeitschrift , 162:39–50, 1978.
Jech, Thomas. Set theory . Academic Press, New York, 1978.
Jech, Thomas. Multiple forcing , volume 88 of Cambridge Tracts in Mathematics . Cambridge University Press, 1986.
Jech, Thomas, Magidor, Menachem, Mitchell, William, and Prikry, Karel. On precipitous ideals. J. of Symb. Logic , 45:1–8, 1980.
Jech, Thomas and Powell, William C.. Standard models of set theory with predication. Bulletin of the AMS , 77(5):808–813, Sep 1971.
Jech, Thomas and Prikry, Karel. On ideals of sets and power set operation. Bull. Amer. Math. Soc , 82:593–595, 1976.
Jech, Thomas and Prikry, Karel. Ideals over uncountable sets: application of almost disjoint functions and generic ultrapowers , volume 214, 18(2) of Amer. Math. Soc. Memoir . AMS, 1979.
Jech, Thomas and Shelah, Saharon. A note on canonical functions. Israel Journal of Mathematics , 68:376–380, 1989.
Jensen, Ronald B.. The fine structure of the constructible hierarchy. Annals of Math. Logic , 4:229–308, 1972.
Judah, Haim and Repicky, Miroslav. No random reals in countable support iterations. Israel Journal of Mathematics , 92:349–359, 1995.
Judah, Haim and Shelah, Saharon. The Kunen-Miller chart (Lebesgue measure, the Baire property, Laver reals and preservation theorems for forcing). The Journal of Symbolic Logic , 55:909–927, 1990.
Judah, Haim, Shelah, Saharon, and Woodin, Hugh. The Borel conjecture. Annals of Pure and Applied Logic , 50:255–269, 1990. Correction of third section has appeared in the book by Bartoszynski and Judah.
Just, Winfried. A modification of Shelah's oracle-cc with applications. Transactions of the AMS , 329:325–356, 1992.
Komjath, Peter. Set systems with finite chromatic number. European Journal of Combinatorics , 10:543–549, 1989.
Kunen, Kenneth. Set Theory: An introduction to independence proofs , volume 102 of Studies in Logic and the Foundations of Mathematics . North-Holland Publishing Co, 1983.
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Kurepa, C.. Transformations monotones des ensembles partiellement ordonne. C.R. Acad. Sci. Paris , 205:1033–1035, 1937.
Laver, Richard. On the consistency of Borel's conjecture. Ada Math. , 137:151–169, 1976.
Laver, Richard. Making supercompact indestructible under κ-directed forcing. Israel J. of Math. , 29:385–388, 1978.
Laver, Richard. Saturated ideals and nonregular ultrafilters. In Procedings of the Bernays Conference 1980, Pabras, Greece . North Holland, 1982.
Laver, Richard and Shelah, Saharon. The N 2-Souslin hypothesis. Transactions of the American Mathematical Society , 264:411–417, 1981.
Magidor, Menachem. On the singular cardinals problem I. Israel J. Math. , 28:1–31, 1977.
Magidor, Menachem. Changing cofinality of cardinals. Fund. Math. , XCIX:61–71, 1978.
Magidor, Menachem. Precipitous ideals and Σ 1 4 sets. Israel J. of Math. , 35:109–134, 1980.
Martin, Donald and Solovay, Robert M.. Internal Cohen extensions. Annals of Math Logic , 2:143–178, 1970.
Martin, Donald A.. Borel Determinacy. Annals of Mathematics , 102:363–371, 1975.
Mathias, A.. Happy families. Annals of Mathematical Logic , 12:59–111, 1977.
Mekler, Alan H.. Finitely additive measures on N and the additive property. Proceedings of the American Mathematical Society , 92:439–444, 1984.
Mekler, Alan H., Roslanowski, Andrzej, and Shelah, Saharon. On the p-rank of Ext. Israel Journal of Mathematics (submitted).
Mekler, Alan H. and Shelah, Saharon. Diamond and λ-systems. Fundamenta Mathematicae , 131:45–51, 1988.
Mekler, Alan H. and Shelah, Saharon. Uniformization principles. The Journal of Symbolic Logic , 54:441–459, 1989.
Milner, Eric and Rado, Richard. The pigeon-hole principle for ordinal numbers. Proc. London Math. Soc , 15:750–768, 1965.
Mitchell, William. Aronszajn trees and the independence of the transfer property. Annals of Mathematical Logic , 5:21–46, 1972/73.
Namba, Kanji. Independence proof of (ω, ωα)-distributive law in complete Boolean algebras. Comment Math. Univ. St. Pauli , 19:1–12, 1970.
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Oxtoby, John C.. Measure and Category . Springer, 1980.
Prikry, Karel. Changing measurable to accessible cardinals. Rozprawy Matematyczne , LXVIII: 5–52, 1970.
Roslanowski, Andrzej and Shelah, Saharon. Norms on possibilities I: forcing with trees and creatures. Memoirs of the AMS (accepted).
Rubin, Matatyahu and Shelah, Saharon. Combinatorial problems on trees: partitions, ∆-systems and large free subtrees. Annals of Pure and Applied Logic , 33:43–81, 1987.
Sageev, G. and Shelah, Saharon. Weak compactness and the structure of Ext(A, Z). In Abelian group theory (Oberwolfach, 1981) , volume 874 of Lecture Notes in Mathematics, pages 87–92. Springer, Berlin New York, 1981, ed. Goebel, R. and Walker, A.E.
Sageev, G. and Shelah, Saharon. On the structure of Ext (A, Z) in ZFC+ . The Journal of Symbolic Logic , 50:302–315, 1985.
Shelah, Saharon. A more general iterable condition ensuring N 1 is not collapsed, II. preprint.
Shelah, Saharon. Categoricity of an abstract elementary class in two successive cardinals. Israel Journal of Mathematics (submitted).
Shelah, Saharon.Non-elementary proper forcing notions. In preparation.
Shelah, Saharon. Not collapsing cardinals ≤ κ in (< κ) –support iterations. In preparation.
Shelah, Saharon. On CS iterations not adding reals. In preparation.
Shelah, Saharon. The Generalized Continuum Hypothesis revisited. Israel Journal of Mathematics (submitted).
Shelah, Saharon. There may be no nowhere dense ultrafilter. In Proceedings of the Logic Colloquium Haifa–95 (accepted). Springer.
Shelah, Saharon. Uniformization. Preprint.
Shelah, Saharon. Infinite abelian groups, Whitehead problem and some constructions. Israel Journal of Mathematics , 18:243–256, 1974.
Shelah, Saharon. A compactness theorem for singular cardinals, free algebras, Whitehead problem and transversals. Israel Journal of Mathematics , 21:319–349, 1975.
Shelah, Saharon. Whitehead groups may be not free, even assuming CH. I. Israel Journal of Mathematics , 28:193–204, 1977.
Shelah, Saharon. A weak generalization of MA to higher cardinals. Israel Journal of Mathematics , 30:297–306, 1978.
Shelah, Saharon. Models with second-order properties. II. Trees with no undefined branches. Annals of Mathematical Logic , 14:73–87, 1978.
Shelah, Saharon. Independence results. The Journal of Symbolic Logic , 45:563–573, 1980.
Shelah, Saharon. Whitehead groups may not be free, even assuming CH. II. Israel Journal of Mathematics , 35:257–285, 1980.
Shelah, Saharon. Free limits of forcing and more on Aronszajn trees. Israel Journal of Mathematics , 38:315–334, 1981.
Shelah, Saharon. Iterated forcing and changing cofinalities. Israel Journal of Mathematics , 40:1–32, 1981.
Shelah, Saharon. Models with second order properties. III. Omitting types for L(Q) . Archiv fur Mathematische Logik und Grundlagenforschung , 21:1–11, 1981.
Shelah, Saharon. On endo-rigid, strongly N 1-free abelian groups in N 1 . Israel Journal of Mathematics , 40:291–295, 1981.
Shelah, Saharon. On Fleissner's diamond. Notre Dame Journal of Formal Logic , 22:29–35, 1981.
Shelah, Saharon. The consistency of Ext(G, Z) = Q . Israel Journal of Mathematics , 39:74–82, 1981.
Shelah, Saharon. Proper forcing , volume 940 of Lecture Notes in Mathematics. Springer-Verlag, Berlin-New York, xxix+496 pp, 1982.
Shelah, Saharon. Classification theory for nonelementary classes, I. The number of uncountable models of ψ∈ Lω1 , ω . Part A. Israel Journal of Mathematics , 46:212–240, 1983.
Shelah, Saharon. Classification theory for nonelementary classes, I. The number of uncountable models of ψ ∈ Lω1 , ω. Part B. Israel Journal of Mathematics , 46:241–273, 1983.
Shelah, Saharon. Constructions of many complicated uncountable structures and Boolean algebras. Israel Journal of Mathematics , 45:100–146, 1983.
Shelah, Saharon. Lifting problem of the measure algebra. Israel Journal of Mathematics , 45:90–96, 1983.
Shelah, Saharon. Models with second order properties. IV. A general method and eliminating diamonds. Annals of Pure and Applied Logic , 25:183–212, 1983.
Shelah, Saharon. Can you take Solovay's inaccessible away? Israel Journal of Mathematics , 48:1–47, 1984.
Shelah, Saharon. Diamonds, uniformization. The Journal of Symbolic Logic , 49: 1022–1033, 1984.
Shelah, Saharon. More on proper forcing. The Journal of Symbolic Logic , 49:1034–1038, 1984.
Shelah, Saharon. On cardinal invariants of the continuum. In Axiomatic set theory (Boulder, Colo., 1983) , volume 31 of Contemp. Mathematics , pages 183–207. Amer. Math. Soc, Providence, RI, 1984. Proceedings of the Conference in Set Theory, Boulder, June 1983; ed. Baumgartner, J., Martin, D. and Shelah, S.
Shelah, Saharon. More on the weak diamond. Annals of Pure and Applied Logic , 28:315–318, 1985.
Shelah, Saharon. On normal ideals and Boolean algebras. In Around classification theory of models , volume 1182 of Lecture Notes in Mathematics, pages 247–259. Springer, Berlin, 1986.
Shelah, Saharon. Classification of nonelementary classes. II. Abstract elementary classes. In Classification theory (Chicago, IL, 1985) , volume 1292 of Lecture Notes in Mathematics, pages 419–497. Springer, Berlin, 1987. Proceedings of the USA-Israel Conference on Classification Theory, Chicago, December 1985; ed. Baldwin, J.T.
Shelah, Saharon. Iterated forcing and normal ideals on ω 1 . Israel Journal of Mathematics , 60:345–380, 1987.
Shelah, Saharon. Semiproper forcing axiom implies Martin maximum but not PFA+ . The Journal of Symbolic Logic , 52:360–367, 1987.
Shelah, Saharon. Uncountable groups have many nonconjugate subgroups. Annals of Pure and Applied Logic, 36:153–206, 1987.
Shelah, Saharon. Some notes on iterated forcing with 2 N0 > N 2 . Notre Dame Journal of Formal Logic , 29:1–17, 1988.
Shelah, Saharon. Was Sierpiński right? I. Israel Journal of Mathematics , 62:355–380, 1988.
Shelah, Saharon. Baire irresolvable spaces and lifting for a layered ideal. Topology and its Applications , 33:217–221, 1989.
Shelah, Saharon. Reflecting stationary sets and successors of singular cardinals. Archive for Mathematical Logic , 31:25–53, 1991.
Shelah, Saharon. Cardinal arithmetic for skeptics. American Mathematical Society. Bulletin. New Series , 26:197–210, 1992.
Shelah, Saharon. CON. Archive for Mathematical Logic , 31:433–443, 1992.
Shelah, Saharon. Viva la difference I: Nonisomorphism of ultra-powers of countable models. In Set Theory of the Continuum , volume 26 of Mathematical Sciences Research Institute Publications, pages 357–405. Springer Verlag, 1992.
Shelah, Saharon. Advances in Cardinal Arithmetic. In Finite and Infinite Combinatorics in Sets and Logic , pages 355–383. Kluwer Academic Publishers, 1993. Sauer, N.W. et al (eds.).
Shelah, Saharon. Cardinal Arithmetic , volume 29 of Oxford Logic Guides . Oxford University Press, 1994.
Shelah, Saharon. Further cardinal arithmetic. Israel Journal of Mathematics , 95:61–114, 1996.
Shelah, Saharon and Stanley, Lee. Generalized Martin's axiom and Souslin's hypothesis for higher cardinals. Israel Journal of Mathematics , 43:225–236, 1982.
Shelah, Saharon and Stanley, Lee. Corrigendum to: “Generalized Martin's axiom and Souslin's hypothesis for higher cardinals” [Israel Journal of Mathematics 43 (1982), no. 3, 225–236; MR 84h:03120]. Israel Journal of Mathematics , 53:304–314, 1986.
Shelah, Saharon and Steprans, Juris. PFA implies all automorphisms are trivial. Proceedings of the American Mathematical Society , 104:1220–1225, 1988.
Shelah, Saharon and Steprans, Juris. Nontrivial homeomorphisms of β N\N without the continuum hypothesis. Fundamenta Mathematicae , 132:135–141, 1989.
Shelah, Saharon and Steprans, Juris. Somewhere trivial automorphisms. Journal of the London Mathematical Society , 49:569–580, 1994.
Shelah, Saharon and Woodin, Hugh. Large cardinals imply that every reasonably definable set of reals is Lebesgue measurable. Israel Journal of Mathematics , 70:381–394, 1990.
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For the reader's convenience we list here again all references to papers of the author, this time sorted by number.
Shelah, Saharon. Proper forcing , volume 940 of Lecture Notes in Mathematics. Springer-Verlag, Berlin-New York, xxix+496 pp, 1982.
Shelah, Saharon. Cardinal Arithmetic , volume 29 of Oxford Logic Guides . Oxford University Press, 1994.
Shelah, Saharon. Infinite abelian groups, Whitehead problem and some constructions. Israel Journal of Mathematics , 18:243–256, 1974.
Shelah, Saharon. A compactness theorem for singular cardinals, free algebras, Whitehead problem and transversals. Israel Journal of Mathematics , 21:319–349, 1975.
Shelah, Saharon. Whitehead groups may be not free, even assuming CH. I. Israel Journal of Mathematics , 28:193–204, 1977.
Devlin, Keith J. and Shelah, Saharon. A weak version of ◊ which follows from 2 N0 > 2 N1 . Israel Journal of Mathematics , 29:239–247, 1978.
Shelah, Saharon. Models with second-order properties. II. Trees with no undefined branches. Annals of Mathematical Logic , 14:73–87, 1978.
Shelah, Saharon. A weak generalization of MA to higher cardinals. Israel Journal of Mathematics , 30:297–306, 1978.
Avraham, Uri (Abraham), Devlin, Keith J., and Shelah, Saharon. The consistency with CH of some consequences of Martin's axiom plus 2 N0 > N 1 . Israel Journal of Mathematics , 31:19–33, 1978.
Shelah, Saharon. Models with second order properties. III. Omitting types for L(Q) . Archiv fur Mathematische Logik und Grundlagenforschung , 21:1–11, 1981.
Devlin, Keith J. and Shelah, Saharon. A note on the normal Moore space conjecture. Canadian Journal of Mathematics. Journal Canadien de Mathematiques , 31:241–251, 1979.
Shelah, Saharon. Classification theory for nonelementary classes, I. The number of uncountable models of ψ∈ Lω1 , ω . Part A. Israel Journal of Mathematics , 46:212–240, 1983.
Shelah, Saharon. Classification theory for nonelementary classes, I. The number of uncountable models of ψ∈ Lω1 , ω . Part B. Israel Journal of Mathematics , 46:241–273, 1983.
Shelah, Saharon. Classification of nonelementary classes. II. Abstract elementary classes. In Classification theory (Chicago, IL, 1985), volume 1292 of Lecture Notes in Mathematics, pages 419–497. Springer, Berlin, 1987. Proceedings of the USA-Israel Conference on Classification Theory, Chicago, December 1985; ed. Baldwin, J.T.
Hiller, Howard L., Huber, Martin, and Shelah, Saharon. The structure of Ext(A, Z) and V = L. Mathematische Zeitschrift , 162:39–50, 1978.
Shelah, Saharon. Whitehead groups may not be free, even assuming CH. II. Israel Journal of Mathematics , 35:257–285, 1980.
Harrington, Leo and Shelah, Saharon. Some exact equiconsistency results in set theory. Notre Dame Journal of Formal Logic , 26:178–188, 1985. Proceedings of the 1980/1 Jerusalem Model Theory year.
Shelah, Saharon. Independence results. The Journal of Symbolic Logic , 45:563–573, 1980.
Avraham, Uri (Abraham) and Shelah, Saharon. Forcing with stable posets. The Journal of Symbolic Logic , 47:37–42, 1982.
Laver, Richard and Shelah, Saharon. The N 2-Souslin hypothesis. Transactions of the American Mathematical Society , 264:411–417, 1981.
Avraham, Uri (Abraham) and Shelah, Saharon. Martin's axiom does not imply that every two N 1-dense sets of reals are isomorphic. Israel Journal of Mathematics , 38:161–176, 1981.
Shelah, Saharon. Models with second order properties. IV. A general method and eliminating diamonds. Annals of Pure and Applied Logic , 25:183–212, 1983.
Abraham, Uri and Shelah, Saharon. Isomorphism types of Aronszajn trees. Israel Journal of Mathematics , 50:75–113, 1985.
Rubin, Matatyahu and Shelah, Saharon. Combinatorial problems on trees: partitions, ∆-systems and large free subtrees. Annals of Pure and Applied Logic , 33:43–81, 1987.
Shelah, Saharon. Iterated forcing and changing cofinalities. Israel Journal of Mathematics , 40:1–32, 1981.
Shelah, Saharon. Free limits of forcing and more on Aronszajn trees. Israel Journal of Mathematics , 38:315–334, 1981.
Shelah, Saharon. On Fleissner's diamond. Notre Dame Journal of Formal Logic , 22:29–35, 1981.
Shelah, Saharon. The consistency of Ext(G, Z) = Q . Israel Journal of Mathematics , 39:74–82, 1981.
Shelah, Saharon. Constructions of many complicated uncountable structures and Boolean algebras. Israel Journal of Mathematics , 45:100–146, 1983.
Sageev, G. and Shelah, Saharon. On the structure of Ext(A, Z) in ZFC+ . The Journal of Symbolic Logic , 50:302–315, 1985.
Shelah, Saharon. On endo-rigid, strongly N 1-free abelian groups in N 1 . Israel Journal of Mathematics , 40:291–295, 1981.
Abraham, Uri and Shelah, Saharon. Forcing closed unbounded sets. The Journal of Symbolic Logic , 48:643–657, 1983.
Sageev, G. and Shelah, Saharon. Weak compactness and the structure of Ext (A, Z). In Abelian group theory (Oberwolfach, 1981) , volume 874 of Lecture Notes in Mathematics, pages 87–92. Springer, Berlin-New York, 1981. ed. Goebel, R. and Walker, A.E.
Shelah, Saharon and Stanley, Lee. Generalized Martin's axiom and Souslin's hypothesis for higher cardinals. Israel Journal of Mathematics , 43:225–236, 1982.
Shelah, Saharon and Stanley, Lee. Corrigendum to: “Generalized Martin's axiom and Souslin's hypothesis for higher cardinals” [Israel Journal of Mathematics 43 (1982), no. 3, 225–236; MR 84h:03120]. Israel Journal of Mathematics , 53:304–314, 1986.
Hart, Bradd, Laflamme, Claude, and Shelah, Saharon. Models with second order properties, V: A General principle. Annals of Pure and Applied Logic, 64:169–194, 1993.
Shelah, Saharon. Can you take Solovay's inaccessible away? Israel Journal of Mathematics , 48:1–47, 1984.
Shelah, Saharon. More on proper forcing. The Journal of Symbolic Logic , 49:1034–1038, 1984.
Shelah, Saharon. Lifting problem of the measure algebra. Israel Journal of Mathematics , 45:90–96, 1983.
Shelah, Saharon. Diamonds, uniformization. The Journal of Symbolic Logic , 49:1022–1033, 1984.
Gitik, Moti and Shelah, Saharon. On the II-condition. Israel Journal of Mathematics , 48:148–158, 1984.
Shelah, Saharon. Uncountable groups have many nonconjugate subgroups. Annals of Pure and Applied Logic , 36:153–206, 1987.
Shelah, Saharon. On cardinal invariants of the continuum. In Axiomatic set theory (Boulder, Colo., 1983), volume 31 of Contemp. Mathematics , pages 183–207. Amer. Math. Soc, Providence, RI, 1984. Proceedings of the Conference in Set Theory, Boulder, June 1983; ed. Baumgartner, J., Martin, D. and Shelah, S.
Shelah, Saharon. More on the weak diamond. Annals of Pure and Applied Logic , 28:315–318, 1985.
Shelah, Saharon. On normal ideals and Boolean algebras. In Around classification theory of models , volume 1182 of Lecture Notes in Mathematics, pages 247–259. Springer, Berlin, 1986.
Foreman, Matthew, Magidor, Menachem, and Shelah, Saharon. Martin's maximum, saturated ideals, and nonregular ultrafilters. I. Annals of Mathematics. Second Series , 127:1–47, 1988.
Shelah, Saharon and Woodin, Hugh. Large cardinals imply that every reasonably definable set of reals is Lebesgue measurable. Israel Journal of Mathematics , 70:381–394, 1990.
Blass, Andreas and Shelah, Saharon. There may be simple P N1-and P N2-Points and the Rudin-Keisler ordering may be downward directed. Annals of Pure and Applied Logic , 33:213–243, 1987.
Shelah, Saharon. Some notes on iterated forcing with 2 N0 > N 2 Notre Dame Journal of Formal Logic , 29:1–17, 1988.
Foreman, Matthew, Magidor, Menachem, and Shelah, Saharon. Martin's maximum, saturated ideals and nonregular ultrafilters. II. Annals of Mathematics. Second Series , 127:521–545, 1988. Will reapeare (in a revised form) in chapter XIII of [Sh f].
Shelah, Saharon. Iterated forcing and normal ideals on ω 1 . Israel Journal of Mathematics , 60:345–380, 1987.
Shelah, Saharon. Semiproper forcing axiom implies Martin maximum but not PFA+ . The Journal of Symbolic Logic , 52:360–367, 1987.
Shelah, Saharon. Baire irresolvable spaces and lifting for a layered ideal. Topology and its Applications , 33:217–221, 1989.
Mekler, Alan H. and Shelah, Saharon. Uniformization principles. The Journal of Symbolic Logic , 54:441–459, 1989.
Shelah, Saharon. Was Sierpiński right? I. Israel Journal of Mathematics , 62:355–380, 1988.
Shelah, Saharon and Steprans, Juris. Nontrivial homeomorphisms of β N \ N without the continuum hypothesis. Fundamenta Mathematicae , 132:135–141, 1989.
Grossberg, Rami and Shelah, Saharon. On the structure of Ext p (G,Z). Journal of Algebra , 121:117–128, 1989.
Judah, Haim and Shelah, Saharon. The Kunen-Miller chart (Lebesgue measure, the Baire property, Laver reals and preservation theorems for forcing). The Journal of Symbolic Logic , 55:909–927, 1990.
Gitik, Moti and Shelah, Saharon. Cardinal preserving ideals. Journal of Symbolic Logic, submitted.
Shelah, Saharon. A more general iterable condition ensuring N 1 is not collapsed, II. preprint.
Mekler, Alan H. and Shelah, Saharon. Diamond and λ-systems. Fundamenta Mathematicae , 131:45–51, 1988.
Mekler, Alan H., Roslanowski, Andrzej, and Shelah, Saharon. On the p-rank of Ext. Israel Journal of Mathematics, submitted.
Shelah, Saharon and Steprans, Juris. PFA implies all automorphisms are trivial. Proceedings of the American Mathematical Society , 104:1220–1225, 1988.
Shelah, Saharon. Viva la difference I: Nonisomorphism of ultra-powers of countable models. In Set Theory of the Continuum , volume 26 of Mathematical Sciences Research Institute, pages 357–405. Springer Verlag, 1992.
Judah, Haim, Shelah, Saharon, and Woodin, Hugh. The Borel conjecture. Annals of Pure and Applied Logic , 50:255–269, 1990. Correction of third section has appeared in the book by Bartoszynski and Judah.
Shelah, Saharon. Reflecting stationary sets and successors of singular cardinals. Archive for Mathematical Logic , 31:25–53, 1991.
Jech, Thomas and Shelah, Saharon. A note on canonical functions. Israel Journal of Mathematics , 68:376–380, 1989.
Shelah, Saharon. Cardinal arithmetic for skeptics. American Mathematical Society. Bulletin. New Series , 26:197–210, 1992.
Abraham, Uri and Shelah, Saharon. A Δ2 2 well-order of the reals and incompactness of L(QMM) . Annals of Pure and Applied Logic , 59:1–32, 1993.
Fremlin, David H. and Shelah, Saharon. Pointwise compact and stable sets of measurable functions. Journal of Symbolic Logic , 58:435–455, 1993.
Shelah, Saharon. CON. Archive for Mathematical Logic , 31:433–443, 1992.
Shelah, Saharon. Advances in Cardinal Arithmetic. In Finite and Infinite Combinatorics in Sets and Logic , pages 355–383. Kluwer Academic Publishers, 1993. Sauer, N.W. et al (eds.).
Shelah, Saharon and Steprans, Juris. Somewhere trivial automorphisms. Journal of the London Mathematical Society, 49:569–580, 1994.
Shelah, Saharon. Further cardinal arithmetic. Israel Journal of Mathematics , 95:61–114, 1996.
Burke, Max R. and Shelah, Saharon. Linear liftings for non complete probability space. Israel Journal of Mathematics , 79:289–296, 1992.
Eklof, Paul C., Mekler, Alan H., and Shelah, Saharon. Uniformization and the diversity of Whitehead groups. Israel Journal of Mathematics , 80:301–321, 1992.
Eklof, Paul C., Mekler, Alan H., and Shelah, Saharon. Hereditarily separable groups and monochromatic uniformization. Israel Journal of Mathematics , 88:213–235, 1994.
Shelah, Saharon. The Generalized Continuum Hypothesis revisited. Israel Journal of Mathematics , submitted.
Roslanowski, Andrzej and Shelah, Saharon. Norms on possibilities I: forcing with trees and creatures. Memoirs of the AMS, accepted.
Shelah, Saharon. Uniformization. preprint.
Eklof, Paul C. and Shelah, Saharon. A Combinatorial Principle Equivalent to the Existence of Non-free Whitehead Groups. In Abelian group theory and related topics , volume 171 of Contemporary Mathematics, pages 79–98. American Mathematical Society, Providence, RI, 1994. edited by Goebel, R., Hill, P. and Liebert, W., Oberwolfach proceedings.
Fuchino, Sakaé, Shelah, Saharon, and Soukup, Lajos. Sticks and clubs, preprint.
Shelah, Saharon. Categoricity of an abstract elementary class in two successive cardinals. Israel Journal of Mathematics, submitted.
Shelah, Saharon. Not collapsing cardinals ≤ κ in (< κ)–support iterations, in preparation.
Shelah, Saharon. There may be no nowhere dense ultrafilter. In Proceedings of the Logic Colloquium Haifa–95 , accepted. Springer.
Džamonja, Mirna and Shelah, Saharon. ♣ does not imply the existence of a Suslin tree. Israel Journal of Mathematics , submitted.
Shelah, Saharon. Non-elementary proper forcing notions, in preparation.
Shelah, Saharon. On CS iterations not adding reals, in preparation.

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