The strength of the projective Martin conjecture
C. T. Chong ; Wei Wang ; Liang Yu
Fundamenta Mathematicae, Tome 209 (2010), p. 21-27 / Harvested from The Polish Digital Mathematics Library
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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 Π¹2n+1 functions is equivalent over ZFC to Σ¹2n+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.

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:283131 
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     year = {2010},
     pages = {21-27},
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C. T. Chong; Wei Wang; Liang Yu. The strength of the projective Martin conjecture. Fundamenta Mathematicae, Tome 209 (2010) pp. 21-27. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm207-1-2/