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Mice with finitely many Woodin cardinals from optimal determinacy hypotheses

Published:2020-07-27 Issue:Supp01 Volume:20 Page:1950013
ISSN:0219-0613
Container-title:Journal of Mathematical Logic
language:en
Short-container-title:J. Math. Log.

Author:

Müller Sandra¹,Schindler Ralf²,Woodin W. Hugh³

Affiliation:

1. Institute of Mathematics, University of Vienna, Augasse 2-6, UZA 1 - Building 2, 1090 Vienna, Austria

2. Institut für Mathematische Logik und Grundlagenforschung, Universität Münster, Einsteinstr. 62, 48149 Münster, FRG, Germany

3. Department of Mathematics and Department of Philosophy, Harvard University, 2 Arrow Street Room 417, Cambridge, MA 02138, USA

Abstract

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 the Determinacy Transfer Theorem for arbitrary [Formula: see text], namely the statement that [Formula: see text] determinacy implies [Formula: see text] determinacy.

Funder

US National Science Foundation

Publisher

World Scientific Pub Co Pte Lt

Subject

Logic

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219061319500132

Reference49 articles.

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