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The axiom of determinacy implies dependent choice in mice
Mathematical Logic Quarterly 65 (3):370-375 (2019)
Abstract
We show that the Axiom of Dependent Choice,, holds in countably iterable, passive premice constructed over their reals which satisfy the Axiom of Determinacy,, in a background universe. This generalizes an argument of Kechris for using Steel's analysis of scales in mice. In particular, we show that for any and any countable set of reals A so that and, we have that.Author's Profile
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References found in this work
Deconstructing inner model theory.Ralf-Dieter Schindler, John Steel & Martin Zeman - 2002 - Journal of Symbolic Logic 67 (2):721-736.
The axiom of determinancy implies dependent choices in l(r).Alexander S. Kechris - 1984 - Journal of Symbolic Logic 49 (1):161 - 173.
The real core model and its scales.Daniel W. Cunningham - 1995 - Annals of Pure and Applied Logic 72 (3):213-289.
The consistency strength of long projective determinacy.Juan P. Aguilera & Sandra Müller - 2019 - Journal of Symbolic Logic 85 (1):338-366.
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