Journal of Mathematical Logic 20 (Supp01):1950013 (2020)

Sandra Eleonore Müller
Ludwig Maximilians Universität, München
W. Hugh Woodin
Harvard University
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.
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DOI 10.1142/s0219061319500132
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References found in this work BETA

Analytic Determinacy and 0#. [REVIEW]Leo Harrington - 1978 - Journal of Symbolic Logic 43 (4):685 - 693.
The Fine Structure of the Constructible Hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
Inner Models with Many Woodin Cardinals.J. R. Steel - 1993 - Annals of Pure and Applied Logic 65 (2):185-209.
Projectively Well-Ordered Inner Models.J. R. Steel - 1995 - Annals of Pure and Applied Logic 74 (1):77-104.
Optimal Proofs of Determinacy.Itay Neeman - 1995 - Bulletin of Symbolic Logic 1 (3):327-339.

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Citations of this work BETA

Long Games and Σ-Projective Sets.Juan P. Aguilera, Sandra Müller & Philipp Schlicht - 2021 - Annals of Pure and Applied Logic 172 (4):102939.
Projective Games on the Reals.Juan P. Aguilera & Sandra Müller - 2020 - Notre Dame Journal of Formal Logic 61 (4):573-589.

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