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https://doi.org/10.4064/fm207-1-2
| Title: | The strength of the projective Martin conjecture | Authors: | Chong, C.T. Wang, W. Yu, L. |
Keywords: | Axiom of determinacy Martin's conjecture Turing cone |
Issue Date: | 2010 | Citation: | Chong, C.T., Wang, W., Yu, L. (2010). The strength of the projective Martin conjecture. Fundamenta Mathematicae 207 (1) : 21-27. ScholarBank@NUS Repository. https://doi.org/10.4064/fm207-1-2 | Abstract: | We show that Martin's conjecture on Π1 1 functions uniformly ≤τ-order preserving on a cone implies Π1 1 Turing Determinacy over ZF + DC. In addition, it is also proved that for n ≥ 0, this conjecture for uniformly degree invariant Π2n+1 1 functions is equivalent over ZFC to Σ2n+2 1-Axiom of Determinacy. As a corollary, the consistency of the conjecture for uniformly degree invariant Π1 1 functions implies the consistency of the existence of a Woodin cardinal. © Instytut Matematyczny PAN, 2010. | Source Title: | Fundamenta Mathematicae | URI: | http://scholarbank.nus.edu.sg/handle/10635/104360 | ISSN: | 00162736 | DOI: | 10.4064/fm207-1-2 |
| Appears in Collections: | Staff Publications |
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