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The Largest Countable Inductive Set is a Mouse Set

Mitch Rudominer
The Journal of Symbolic Logic, 64 (1999), pp. 443-459
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Abstract

We show that the set of reals in the canonical inner model for the theory ZFC - Replacement + "There exists omega Woodin cardinals cofinal in the ordinals" is equal to the largest countable inductive set of reals.