Abstract

We show that Martin’s conjecture on Π1-functions uniformly ≤T -order preserving on a cone implies Π1 Turing Determinacy over ZF+DC. In addition, it is also proved that for n ≥ 0, this conjecture for uniformly degree invariant Π2n+1functions is equivalent over ZFC to Σ2n+2-Axiom of Determinacy. As a corollary, the consistency of the conjecture for Π1-uniformly degree invariant functions implies the consistency of the existence of a Woodin cardinal.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.