Skip to main content Accessibility help
×
Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-12-02T18:19:55.781Z Has data issue: false hasContentIssue false

The pair (Nn, N0) may fail N0-compactness

from ARTICLES

Published online by Cambridge University Press:  31 March 2017

Matthias Baaz
Affiliation:
Technische Universität Wien, Austria
Sy-David Friedman
Affiliation:
Universität Wien, Austria
Jan Krajíček
Affiliation:
Academy of Sciences of the Czech Republic, Prague
Get access
Type
Chapter
Information
Logic Colloquium '01 , pp. 402 - 433
Publisher: Cambridge University Press
Print publication year: 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[Ch] Chen C., Chang, A note on the two cardinal problem,Proceedings of the AmericanMathematical Society, vol. 16 (1965), pp. 1148–1155.
[CK] Chen C., Chang and Jerome H., Keisler, Model Theory, Studies in Logic and the Foundation of Mathematics, vol. 73, North Holland Publishing Co., Amsterdam, 1973.
[CFM] James, Cummings, Matthew, Foreman, and Menachem, Magidor, Squares, scales and stationary reflection,Journal of Mathematical Logic, vol. 1 (2001), pp. 35–98.
[De73] Keith J., Devlin, Aspects of constructibility, Lecture Notes in Mathematics, vol. 354, Springer-Verlag, 1973.
[Fu65] E. G., Furkhen, Languages with added quantifier “there exist at least ℵα,The Theory of Models (J. V., Addison, L. A., Henkin, and A., Tarski, editors), North-Holland Publishing Company, 1965, pp. 121–131.
[GcSh:491] Martin, Gilchrist and Saharon, Shelah, Identities on cardinals less than ℵω,The Journal of Symbolic Logic, vol. 61 (1996), pp. 780–787, math.LO/95052155.
[GcSh:583] Martin, Gilchrist and Saharon, Shelah, The Consistency of ZFC + 2ℵ0 > ℵω + I(ℵ2) = I(ℵω), The Journal of Symbolic Logic, vol. 62 (1997), pp. 1151–1160, math.LO/9603219.
[Jn] Ronald B., Jensen, The fine structure of the constructible hierarchy,Annals ofMathematical Logic, vol. 4 (1972), pp. 229–308.
[Ke66] Jerome H., Keisler, First order properties of pairs of cardinals,Bulletin of the American Mathematical Society, vol. 72 (1966), pp. 141–144.
[Ke66a] Jerome H., Keisler, Some model theoretic results for ω-logic,Israel Journal ofMathematics, vol. 4 (1966), pp. 249–261.
[Mi72] William, Mitchell, Aronszajn trees and the independence of the transfer property,Annals of Mathematical Logic, vol. 5 (1972), no. 3, pp. 21–46.
[Mo68] M. D., Morley, Partitions and models,Proceedings of the Summer School in Logic, Leeds, 1967, Lecture Notes in Mathematics, vol. 70, Springer-Verlag, 1968, pp. 109–158.
[Mo57] Andrzej, Mostowski, On a generalization of quantifiers,Fundamenta Mathematicae, vol. 44 (1957), pp. 12–36.
[MV62] M. D., Morley and R. L., Vaught, Homogeneous and universal models,Mathematica Scandinavica, vol. 11 (1962), pp. 37–57.
[RoSh:733] Andrzej, Rosłanowski and Saharon, Shelah, Historic forcing for Depth,Colloquium Mathematicum, vol. 89 (2001), pp. 99–115, math.LO/0006219.
[Sc74] James H., Schmerl, Generalizing special Aronszajn trees,The Journal of Symbolic Logic, vol. 39 (1974), pp. 732–740.
[Sc85] James H., Schmerl, Transfer theorems and their application to logics,Model Theoretic Logics (J., Barwise and S., Feferman, editors), Springer-Verlag, 1985, pp. 177–209.
[ScSh:20] James H., Schmerl and Saharon, Shelah, On power-like models for hyperinaccessible cardinals,The Journal of Symbolic Logic, vol. 37 (1972), pp. 531–537.
[Sh:8] Saharon, Shelah, Two cardinal compactness,Israel Journal of Mathematics, vol. 9 (1971), pp. 193–198.
[Sh:18] Saharon, Shelah, On models with power-like orderings,The Journal of Symbolic Logic, vol. 37 (1972), pp. 247–267.
[Sh:37] Saharon, Shelah, A two-cardinal theorem,Proceedings of the American Mathematical Society, vol. 48 (1975), pp. 207–213.
[Sh:49] Saharon, Shelah, A two-cardinal theorem and a combinatorial theorem,Proceedings of the American Mathematical Society, vol. 62 (1976), pp. 134–136.
[Sh:74] Saharon, Shelah, Appendix to: “Models with second-order properties. II. Trees with no undefined branches” (Annals ofMathematical Logic vol. 14 (1978), no. 1, pp. 73–87), Annals of Mathematical Logic, vol. 14 (1978), pp. 223–226.
[Sh:289] Saharon, Shelah, Consistency of positive partition theorems for graphs and models,Set theory and its applications (Toronto, ON, 1987) (J., Steprans and S., Watson, editors), Lecture Notes in Mathematics, vol. 1401, Springer, Berlin-New York, 1989, pp. 167–193.
[Sh:269] Saharon, Shelah, “Gap 1” two-cardinal principles and the omitting types theorem for L(Q), Israel Journal of Mathematics, vol. 65 (1989), pp. 133–152.
[Sh:288] Saharon, Shelah, Strong partition relations below the power set: Consistency, Was Sierpínski right, II?,Proceedings of the Conference on Set Theory and its Applications in honor of A. Hajnal and V. T. Sos, Budapest, 1/91, ColloquiaMathematica Societatis Janos Bolyai. Sets, Graphs, and Numbers, vol. 60, 1991, math.LO/9201244, pp. 637–638.Google Scholar
[Sh:424] Saharon, Shelah, On CH + 2ℵ1 (a)2/2 for a < ω2, Logic Colloquium –90. ASL Summer Meeting in Helsinki, Lecture Notes in Logic, vol. 2, Springer Verlag, 1993, math.LO/9308212, pp. 281–289.
[Sh:522] Saharon, Shelah, Borel sets with large squares,Fundamenta Mathematicae, vol. 159 (1999), pp. 1–50, math.LO/9802134.
[Sh:546] Saharon, Shelah, Was Sierpinski right? IV,The Journal of Symbolic Logic, vol. 65 (2000), pp. 1031–1054, math.LO/9712282.
[Sh:824] Saharon, Shelah, Two cardinals models with gap one revisited,Mathematical Logic Quarterly, to appear.
[Sh:E17] Saharon, Shelah, Two cardinal and power like models: compactness and large group of automorphisms,Notices of the AmericanMathematical Society, vol. 18 (1968), p. 425.
[Sh:E28] Saharon, Shelah, Details on [Sh:74].
[ShVa:790] Saharon, Shelah and Jouko, Väänänen, Recursive logic frames, Preprint.
[Si71] Jack, Silver, Some applications of model theory in set theory,Annals of Mathematical Logic, vol. 3 (1971), pp. 45–110.
[Va65] R. L., Vaught, A Löwenheim-Skolem theorem for cardinals far apart,The Theory of Models (J. V., Addison, L. A., Henkin, and A., Tarski, editors), North-Holland Publishing Company, 1965, pp. 81–89.

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×