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  1. Home
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  3. The Core Model Iterability Problem
  • Cited by 2
Publisher:
Cambridge University Press
Online publication date:
March 2017
Print publication year:
2017
Online ISBN:
9781316716892
DOI:
https://doi.org/10.1017/9781316716892
Subjects:
Mathematics, Logic, Categories and Sets, Logic, Philosophy, Programming Languages and Applied Logic
Series:
Lecture Notes in Logic (8)
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. Large cardinal hypotheses play a central role in modern set theory. One important way to understand such hypotheses is to construct concrete, minimal universes, or 'core models', satisfying them. Since Gödel's pioneering work on the universe of constructible sets, several larger core models satisfying stronger hypotheses have been constructed, and these have proved quite useful. In this volume, the eighth publication in the Lecture Notes in Logic series, Steel extends this theory so that it can produce core models having Woodin cardinals, a large cardinal hypothesis that is the focus of much current research. The book is intended for advanced graduate students and researchers in set theory.

Reviews

‘Steel's monograph is a masterpiece in terms of both research and exposition. The reviewer ranks it amongst the most significant works in set theory, because of its fundamental advances and broadly applicable new methods. It is required reading for anyone wishing to get up to date on core model theory, and it leads to many beautiful open problems for research.'

Ernest Schimmerling Source: Journal of Symbolic Logic

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Contents

Contents
References
References
Dodd, A. J., The core model , London Math. Soc. Lecture notes, vol. 61, 1982.
Dodd, A. J. and Jensen, R. B., The core model , Ann. Math. Logic 20 (1981), 43–75.
Dodd, A. J. and Jensen, R. B., The covering lemma for K , Ann. Math. Logic 22 (1982), 1–30.
Dodd, A. J. and Jensen, R. B., The covering lemma for L[U], Ann. Math. Logic 22 (1982), 127–155.
Dodd, A. J., Jensen, R. B., Koepke, P., and Mitchell, W. J., The core model for nonoverlapping extender sequences , to appear.
Foreman, M., Magidor, M., and Shelah, S., Martin's maximum, saturated ideals, and non-regular ultrafilters , Ann. of Math. (2) 127 (1988), 1–47.
Hauser, K., The consistency strength of projective absoluteness , habilitationsschrift, Ruprecht-Karls-Universitat, Heidelberg, 1993.
Greg, Hjorth, Π1 1 Wadge degrees , Ann. Pure and Applied Logic 77 (1996), no. 1, 53–74.
Kechris, A. S. and Solovay, R. M., On the relative consistency strength of determinacy hypotheses, TAMS, 290 (1), 179–211.
Kunen, K., Some applications of iterated ultrapowers in set theory , Ann. Math. Logic 1 (1970), 179–227.
Kunen, K., Saturated ideals , J. Symbolic Logic 43 (1978), 65–77.
Martin, D. A. and Steel, J. R., Iteration trees , JAMS 7 (1994), 1–73.
Mitchell, W. J., The core model for sequences of measuresl , Math. Proc. Cambridge Philos. Soc. 95 (1984), 228–260.
Mitchell, W. J., Σ3 1 absoluteness for sequences of measures , in Set Theory of the Continuum, Judah, H., Just, W., Woodin, H. eds., MSRI publications, no. 26, Springer-Verlag 1992.
Mitchell, W. J., The core model for sequences of measures II, unpublished.
Mitchell, W. J. and Steel, J. R., Fine structure and iteration trees , Springer Lecture Notes in Logic 3 (1994).
Mitchell, W. J., E. Schimmerling and Steel, J. R., The weak covering lemma up to a Woodin cardinal, to appear in Ann. Pure and Applied Logic.
Schimmerling, E., Combinatorial principles in the core model for one Woodin cardinal , Ann. of Pure and Applied Logic, 74 (1995) 153–201.
Schimmerling, E. and Steel, J. R., Fine structure for tame inner models , J. Symbolic Logic, vol. 61 (1996), 621–639.
Steel, J. R., Core models with more Woodin cardinals, to appear.
Steel, J. R., Protectively wellordered inner models , Ann. of Pure and Applied Logic, vol. 74 (1995), 77–104.
Steel, J. R. and Van Wesep, R., Two consequence of determinacy consistent with choice , Trans, of AMS 272 (1982), 67–85.
Steel, J. R. and Welch, P. D., Σ3 1 absoluteness and the second uniform indiscernible, to appear.
Todorčevic, S., A note on the proper forcing axiom , Contemporary Mathematics 95 (1984), 209–218.
Woodin, W. H., Some consistency results in ZFC using AD , in Cabal Seminar 79-81, Springer Lecture Notes in Mathematics, vol. 1019 (1983), 172–198.

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