The strength of the projective Martin conjecture

C. T. Chong, Wei Wang, and Liang Yu. "The strength of the projective Martin conjecture." Fundamenta Mathematicae 207.1 (2010): 21-27. <http://eudml.org/doc/283131>.

@article{C2010,
abstract = {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 $Π¹_\{2n+1\}$ functions is equivalent over ZFC to $Σ¹_\{2n+2\}$-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.},
author = {C. T. Chong, Wei Wang, Liang Yu},
journal = {Fundamenta Mathematicae},
keywords = {Martin's conjecture; Axiom of Determinacy; consistency; Woodin cardinal; Turing cone},
language = {eng},
number = {1},
pages = {21-27},
title = {The strength of the projective Martin conjecture},
url = {http://eudml.org/doc/283131},
volume = {207},
year = {2010},
}

TY - JOUR
AU - C. T. Chong
AU - Wei Wang
AU - Liang Yu
TI - The strength of the projective Martin conjecture
JO - Fundamenta Mathematicae
PY - 2010
VL - 207
IS - 1
SP - 21
EP - 27
AB - 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 $Π¹_{2n+1}$ functions is equivalent over ZFC to $Σ¹_{2n+2}$-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.
LA - eng
KW - Martin's conjecture; Axiom of Determinacy; consistency; Woodin cardinal; Turing cone
UR - http://eudml.org/doc/283131
ER -