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- W4300248812 abstract "Let kappa be the least ordinal alpha such that L_{alpha}(R) is admissible. Let A be the set of reals x such that x is ordinal definable in L_{alpha}(R), for some alpha<kappa. It is well known that (assuming determinacy) A is the largest countable inductive set of reals. Let T be the following theory: ZFC - Replacement + There exists $omega$ Woodin cardinals which are cofinal in the ordinals. T has consistency strength weaker than that of the theory ZFC + There exists omega Woodin cardinals, but stronger than that of the theory ZFC + There exists n Woodin Cardinals, for each n. Let M be the canonical, minimal inner model for the theory T. In this paper we show that A is equal to the set of reals in M. Since M is a mouse, we say that A is a mouse set. As an application, we use our characterization of A to give an inner-model-theoretic proof of Martin's theorem that A is equal to the set of reals which are Sigma^*_n for some n." @default.
- W4300248812 created "2022-10-03" @default.
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- W4300248812 date "1996-09-15" @default.
- W4300248812 modified "2023-09-26" @default.
- W4300248812 title "The Largest Countable Inductive Set is a Mouse Set" @default.
- W4300248812 doi "https://doi.org/10.48550/arxiv.math/9609205" @default.
- W4300248812 hasPublicationYear "1996" @default.
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