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PCF theory and Woodin cardinals

Published online by Cambridge University Press:  31 March 2017

Zoé Chatzidakis
Affiliation:
Université de Paris VII (Denis Diderot)
Peter Koepke
Affiliation:
Rheinische Friedrich-Wilhelms-Universität Bonn
Wolfram Pohlers
Affiliation:
Westfälische Wilhelms-Universität Münster, Germany
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Logic Colloquium '02 , pp. 172 - 205
Publisher: Cambridge University Press
Print publication year: 2006

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References

[1] U., Abraham and M., Magidor, Cardinal arithmetic Handbook of Set Theory (Foreman, Kanamori, and Magidor, editors), to appear.
[2] M., Burke and M., Magidor, Shelah's pcf theory and its applications Annals of Pure and Applied Logic, vol. 50 (1990), no. 3, pp. 207–254.Google Scholar
[3] K. I., Devlin and R. B., Jensen, Marginalia to a theorem of Silver, ⊢ ISILCLogic Conference, Lecture Notes in Mathematics, vol. 499, Springer, Berlin, 1975, pp. 115–142.
[4] W. B., Easton, Powers of regular cardinals Annals of Pure and Applied Logic, vol. 1 (1970), pp. 139–178.
[5] M., Foreman, M., Magidor, and R., Schindler, The consistency strength of successive cardinals with the tree property The Journal of Symbolic Logic, vol. 66 (2001), no. 4, pp. 1837– 1847.
[6] M., Gitik, The negation of the singular cardinal hypothesis from o(k) = κ++, Annals of Pure and Applied Logic, vol. 43 (1989), no. 3, pp. 209–234.
[7] M., Gitik, The strength of the failure of the singular cardinal hypothesis Annals of Pure and Applied Logic, vol. 51 (1991), no. 3, pp. 215–240.
[8] M., Gitik, Blowing up power of a singular cardinal—wider gaps Annals of Pure and Applied Logic, vol. 116 (2002), no. 1-3, pp. 1–38.
[9] M., Gitik, Two stationary sets with different gaps of the power function, available at http://www.math.tau.ac.il/∼gitik.
[10] M., Gitik, Introduction to prikry type forcing notions Handbook of Set Theory (Foreman, Kanamori, and Magidor, editors), to appear.
[11] M., Gitik and W., Mitchell, Indiscernible sequences for extenders, and the singular cardinal hypothesis Annals of Pure and Applied Logic, vol. 82 (1996), no. 3, pp. 273–316.
[12] K., Hauser and R., Schindler, Projective uniformization revisited Annals of Pure and Applied Logic, vol. 103 (2000), no. 1-3, pp. 109–153.
[13] M., Holz, K., Steffens, and E., Weitz, Introduction to Cardinal Arithmetic, Birkhäuser Verlag, Basel, 1999.
[14] T., Jech, Set Theory, Academic Press, New York, 1978.
[15] T., Jech, Singular cardinals and the PCF theory The Bulletin of Symbolic Logic, vol. 1 (1995), no. 4, pp. 408–424.
[16] M., Magidor, On the singular cardinals problem. I Israel Journal of Mathematics, vol. 28 (1977), no. 1-2, pp. 1–31.
[17] M., Magidor, On the singular cardinals problem. II Annals of Mathematics. Second Series, vol. 106 (1977), no. 3, pp. 517–547.
[18] W., Mitchell and E., Schimmerling, Weak covering without countable closure Mathematical Research Letters, vol. 2 (1995), no. 5, pp. 595–609.
[19] W., Mitchell, E., Schimmerling, and J., Steel, The covering lemma up to a Woodin cardinal Annals of Pure and Applied Logic, vol. 84 (1997), no. 2, pp. 219–255.
[20] W., Mitchell and J., Steel, Fine Structure and Iteration Trees, Lecture Notes in Logic, vol. 3, Springer-Verlag, Berlin, 1994.
[21] K. L., Prikry, Changing measurable into accessible cardinals Dissertationes Mathematicae (Rozprawy Matematyczne), vol. 68 (1970), p. 55.
[22] Th., Räsch and R., Schindler, A new condensation principle Archive for Mathematical Logic, vol. 44 (2005), no. 2, pp. 159–166.
[23] E., Schimmerling and J. R., Steel, The maximality of the core model Transactions of the American Mathematical Society, vol. 351 (1999), no. 8, pp. 3119–3141.
[24] E., Schimmerling and W. H., Woodin, The Jensen covering property The Journal of Symbolic Logic, vol. 66 (2001), no. 4, pp. 1505–1523.
[25] R., Schindler, Mutual stationarity in the core model Logic Colloquium '01 (Baaz et al., editors), Lecture Notes in Logic, vol. 20, ASL, Urbana, IL, 2005, pp. 386–401.Google Scholar
[26] R., Schindler and J., Steel, List of open problems in inner model theory, available at http://wwwmath1.uni-muenster.de/logik/org/staff/rds/list.html.
[27] S., Shelah, Cardinal Arithmetic, The Clarendon Press Oxford University Press, NewYork, 1994.
[28] S., Shelah, Further cardinal arithmetic Israel Journal of Mathematics, vol. 95 (1996), pp. 61– 114.
[29] J., Silver, On the singular cardinals problem Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974), Vol. 1, Canad. Math. Congress, Montreal, Que., 1975, pp. 265–268.Google Scholar
[30] J., Steel, Projectively well-ordered inner models Annals of Pure and Applied Logic, vol. 74 (1995), no. 1, pp. 77–104.
[31] J., Steel, The Core Model Iterability Problem, Lecture Notes in Logic, vol. 8, Springer-Verlag, Berlin, 1996.
[32] J., Steel, Core models with moreWoodin cardinals The Journal of Symbolic Logic, vol. 67 (2002), no. 3, pp. 1197–1226.

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