The strength of choiceless patterns of singular and weakly compact cardinals

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Annals of Pure and Applied Logic 159 (1-2):198-248 (2009)
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Abstract

We extend the core model induction technique to a choiceless context, and we exploit it to show that each one of the following two hypotheses individually implies that , the Axiom of Determinacy, holds in the of a generic extension of : every uncountable cardinal is singular, and every infinite successor cardinal is weakly compact and every uncountable limit cardinal is singular

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10.1016/j.apal.2008.12.001

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Citations of this work

Making all cardinals almost Ramsey.Arthur W. Apter & Peter Koepke - 2008 - Archive for Mathematical Logic 47 (7-8):769-783.
A remark on the tree property in a choiceless context.Arthur W. Apter - 2011 - Archive for Mathematical Logic 50 (5-6):585-590.
Thin equivalence relations and inner models.Philipp Schlicht - 2014 - Annals of Pure and Applied Logic 165 (10):1577-1625.

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References found in this work

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Inner models with many Woodin cardinals.J. R. Steel - 1993 - Annals of Pure and Applied Logic 65 (2):185-209.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
Projectively well-ordered inner models.J. R. Steel - 1995 - Annals of Pure and Applied Logic 74 (1):77-104.

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