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Title: The strength of the projective Martin conjecture
Authors: Chong, C.T. 
Wang, W.
Yu, L.
Keywords: Axiom of determinacy
Martin's conjecture
Turing cone
Issue Date: 2010
Citation: Chong, C.T., Wang, W., Yu, L. (2010). The strength of the projective Martin conjecture. Fundamenta Mathematicae 207 (1) : 21-27. ScholarBank@NUS Repository.
Abstract: We show that Martin's conjecture on Π1 1 functions uniformly ≤τ-order preserving on a cone implies Π1 1 Turing Determinacy over ZF + DC. In addition, it is also proved that for n ≥ 0, this conjecture for uniformly degree invariant Π2n+1 1 functions is equivalent over ZFC to Σ2n+2 1-Axiom of Determinacy. As a corollary, the consistency of the conjecture for uniformly degree invariant Π1 1 functions implies the consistency of the existence of a Woodin cardinal. © Instytut Matematyczny PAN, 2010.
Source Title: Fundamenta Mathematicae
ISSN: 00162736
DOI: 10.4064/fm207-1-2
Appears in Collections:Staff Publications

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