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The strength of the projective Martin conjecture

C. T. Chong;  Wei Wang;  Liang Yu — 2010

Fundamenta Mathematicae

We show that Martin’s conjecture on Π¹₁ functions uniformly ≤ T -order preserving on a cone implies Π¹₁ Turing Determinacy over ZF + DC. In addition, it is also proved that for n ≥ 0, this conjecture for uniformly degree invariant Π ¹ 2 n + 1 functions is equivalent over ZFC to Σ ¹ 2 n + 2 -Axiom of Determinacy. As a corollary, the consistency of the conjecture for uniformly degree invariant Π¹₁ functions implies the consistency of the existence of a Woodin cardinal.

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