The axiom of determinacy implies dependent choice in mice
نویسندگان
چکیده
منابع مشابه
The Axiom of Determinancy Implies Dependent Choices in L(R)
We prove the following Main Theorem: ZF + AD + V L(R) =>DC. As a corollary we have that Con(ZF + AD) Con(ZF + AD + DC). Combined with the result of Woodin that Con(ZF + AD) Con(ZF + AD + AC') it follows that DC (as well as AC') is independent relative to ZF + AD. It is finally shown (jointly with H. Woodin) that ZF + AD + DCR, where DCR is DC restricted to reals, implies the consistency of ZF +...
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Since all known proofs of the NIELSEN-SCHREIER theorem (every subgroup of a free group is free, henceforth denoted by (NS)) make use of the axiom of choice (AC) it is reasonable to conjecture that some form of (AC) is necessary to prove (NS). (See [ l ] , [3], [5] and [S] for several proofs of (NS).) This conjecture was verified by LAUCHLI in [4], where it was shown that the negation of (NS) is...
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We investigate the computational content of the axiom of determinacy (AD) in the setting of classical arithmetic in all finite types with the principle of dependent choices (DC). By employing the notion of realizability interpretation for arithmetic given by Berardi, Bezem and Coquand (1998), we interpret the negative translation of AD. Consequently, the combination of the negative translation ...
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ژورنال
عنوان ژورنال: Mathematical Logic Quarterly
سال: 2019
ISSN: 0942-5616,1521-3870
DOI: 10.1002/malq.201800077