Geodesic
The strength of the projective Martin conjecture
C. T. Chong 1   ; Wei Wang 2   ; Liang Yu 3
1 Department of Mathematics Faculty of Science National University of Singapore Lower Kent Ridge Road Singapore 117543
2 Department of Philosophy Sun Yat-sen University 135 Xingang Xi Road Guangzhou 510275, P.R. China
3 Institute of Mathematical Sciences Nanjing University Nanjing, Jiangsu Province 210093, P.R. China
Fundamenta Mathematicae, Tome 207 (2010) no. 1, pp. 21-27 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We show that Martin's conjecture on $\Pi^1_1$ functions uniformly $\leq_T$-order preserving on a cone implies $\Pi^1_1$ Turing Determinacy over $\hbox{ZF}+{\hbox{DC}}$. In addition, it is also proved that for $n\ge 0$, this conjecture for uniformly degree invariant $\mathbf{\Pi}^1_{2n+1}$ functions is equivalent over ZFC to $\mathbf{\Sigma}^1_{2n+2}$-Axiom of Determinacy. As a corollary, the consistency of the conjecture for uniformly degree invariant $\Pi^1_1$ functions implies the consistency of the existence of a Woodin cardinal.
DOI : 10.4064/fm207-1-2
Keywords: martins conjecture functions uniformly leq t order preserving cone implies turing determinacy hbox hbox addition proved conjecture uniformly degree invariant mathbf functions equivalent zfc mathbf sigma axiom determinacy corollary consistency conjecture uniformly degree invariant functions implies consistency existence woodin cardinal

C. T. Chong  1   ; Wei Wang  2   ; Liang Yu  3

1 Department of Mathematics Faculty of Science National University of Singapore Lower Kent Ridge Road Singapore 117543
2 Department of Philosophy Sun Yat-sen University 135 Xingang Xi Road Guangzhou 510275, P.R. China
3 Institute of Mathematical Sciences Nanjing University Nanjing, Jiangsu Province 210093, P.R. China 
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C. T. Chong; Wei Wang; Liang Yu. The strength of the projective Martin conjecture. Fundamenta Mathematicae, Tome 207 (2010) no. 1, pp. 21-27. doi: 10.4064/fm207-1-2

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