On the relative consistency strength of determinacy hypotheses

Kechris, Alexander S.; Solovay, Robert M.

doi:10.1090/S0002-9947-1985-0787961-2

On the relative consistency strength of determinacy hypotheses
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by Alexander S. Kechris and Robert M. Solovay

Trans. Amer. Math. Soc. 290 (1985), 179-211

DOI: https://doi.org/10.1090/S0002-9947-1985-0787961-2

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Abstract:

For any collection of sets of reals $C$, let $C{\text {-DET}}$ be the statement that all sets of reals in $C$ are determined. In this paper we study questions of the form: For given $C \subseteq C\prime$, when is $C\prime {\text {-DET}}$ equivalent, equiconsistent or strictly stronger in consistency strength than $C {\text {-DET}}$ (modulo ${\text {ZFC}}$)? We focus especially on classes $C$ contained in the projective sets.

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