The strength of the projective Martin conjecture

• Autorzy: C. T. Chong , Wei Wang , Liang Yu
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 28A20: Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
• 03D28: Other Turing degree structures
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 207
• Numer: 1
• Strony: 21-27

Daty

wydano

2010

Twórcy

autor

C. T. Chong

• Department of Mathematics, Faculty of Science, National University of Singapore, Lower Kent Ridge Road, Singapore 117543

autor

Wei Wang

• Department of Philosophy, Sun Yat-sen University, 135 Xingang Xi Road, Guangzhou 510275, P.R. China

autor

Liang Yu

• Institute of Mathematical Sciences, Nanjing University, Nanjing, Jiangsu Province 210093, P.R. China

Identyfikatory

DOI

10.4064/fm207-1-2