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On the prewellorderings associated with the directed systems of mice

Grigor Sargsyan

Journal of Symbolic Logic 78 (3):735-763 (2013)

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Mice with finitely many Woodin cardinals from optimal determinacy hypotheses.Sandra Müller, Ralf Schindler & W. Hugh Woodin - 2020 - Journal of Mathematical Logic 20 (Supp01):1950013.details We prove the following result which is due to the third author. Let [Formula: see text]. If [Formula: see text] determinacy and [Formula: see text] determinacy both hold true and there is no [Formula: see text]-definable [Formula: see text]-sequence of pairwise distinct reals, then [Formula: see text] exists and is [Formula: see text]-iterable. The proof yields that [Formula: see text] determinacy implies that [Formula: see text] exists and is [Formula: see text]-iterable for all reals [Formula: see text]. A consequence is (...) Download Export citation Bookmark 6 citations
Mice with finitely many Woodin cardinals from optimal determinacy hypotheses.Sandra Müller, Ralf Schindler & W. Hugh Woodin - 2020 - Journal of Mathematical Logic 20 (Supp01):1950013.details We prove the following result which is due to the third author. Let [Formula: see text]. If [Formula: see text] determinacy and [Formula: see text] determinacy both hold true and there is no [Formula: see text]-definable [Formula: see text]-sequence of pairwise distinct reals, then [Formula: see text] exists and is [Formula: see text]-iterable. The proof yields that [Formula: see text] determinacy implies that [Formula: see text] exists and is [Formula: see text]-iterable for all reals [Formula: see text]. A consequence is (...) Download Export citation Bookmark 6 citations
An Inner Model Proof of the Strong Partition Property for $delta^{2}_{1}$.Grigor Sargsyan - 2014 - Notre Dame Journal of Formal Logic 55 (4):563-568.details Assuming $V=L+AD$, using methods from inner model theory, we give a new proof of the strong partition property for ${\sim}{ \delta }^{2}_{1}$. The result was originally proved by Kechris et al. Download Export citation Bookmark

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