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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the relative consistency strength of determinacy hypotheses


Authors: Alexander S. Kechris and Robert M. Solovay
Journal: Trans. Amer. Math. Soc. 290 (1985), 179-211
MSC: Primary 03E60; Secondary 03E15, 03E35
MathSciNet review: 787961
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0787961-2
PII: S 0002-9947(1985)0787961-2
Article copyright: © Copyright 1985 American Mathematical Society