Some applications of short core models

Annals of Pure and Applied Logic 37 (2):179-204 (1988)

Abstract

We survey the definition and fundamental properties of the family of short core models, which extend the core model K of Dodd and Jensen to include α-sequences of measurable cardinals . The theory is applied to various combinatorial principles to get lower bounds for their consistency strengths in terms of the existence of sequences of measurable cardinals. We consider instances of Chang's conjecture, ‘accessible’ Jónsson cardinals, the free subset property for small cardinals, a canonization property of ω ω , and a non-closure property of elementary embeddings of the universe. In some cases, equiconsistencies are obtained

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References found in this work

The Core Model.A. Dodd & R. Jensen - 1981 - Annals of Mathematical Logic 20 (1):43-75.
Sets Constructible From Sequences of Ultrafilters.William J. Mitchell - 1974 - Journal of Symbolic Logic 39 (1):57-66.
The Consistency Strength of the Free-Subset Property for Ωω.Peter Koepke - 1984 - Journal of Symbolic Logic 49 (4):1198 - 1204.
The Covering Lemma for L[U].A. J. Dodd & R. B. Jensen - 1982 - Annals of Mathematical Logic 22 (2):127-135.
Sets Constructed From Sequences of Measures: Revisited.William J. Mitchell - 1983 - Journal of Symbolic Logic 48 (3):600-609.

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Citations of this work

Measurable Cardinals and Good Σ1-Wellorderings.Philipp Lücke & Philipp Schlicht - 2018 - Mathematical Logic Quarterly 64 (3):207-217.
On the Free Subset Property at Singular Cardinals.Peter Koepke - 1989 - Archive for Mathematical Logic 28 (1):43-55.
Co-Stationarity of the Ground Model.Natasha Dobrinen & Sy-David Friedman - 2006 - Journal of Symbolic Logic 71 (3):1029 - 1043.
More Canonical Forms and Dense Free Subsets.Heike Mildenberger - 2004 - Annals of Pure and Applied Logic 125 (1-3):75-99.

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