Please use this identifier to cite or link to this item: https://doi.org/10.1090/S0002-9947-09-04783-7
Title: A π1 1-uniformization principle for reals
Authors: Chong, C.T. 
Yu, L.
Issue Date: Aug-2009
Citation: Chong, C.T., Yu, L. (2009-08). A π1 1-uniformization principle for reals. Transactions of the American Mathematical Society 361 (8) : 4233-4245. ScholarBank@NUS Repository. https://doi.org/10.1090/S0002-9947-09-04783-7
Abstract: We introduce a Π1 1-uniformization principle and establish its equivalence with the set-theoretic hypothesis (ω 1)L= ω1. This principle is then applied to derive the equivalence, to suitable set-theoretic hypotheses, of the existence of Π1 1-maximal chains and thin maximal antichains in the Turing degrees. We also use the Π1 1-uniformization principle to study Martin's conjectures on cones of Turing degrees, and show that under V = L the conjectures fail for uniformly degree invariant Π1 1 functions. © 2009 American Mathematical Society.
Source Title: Transactions of the American Mathematical Society
URI: http://scholarbank.nus.edu.sg/handle/10635/102786
ISSN: 00029947
DOI: 10.1090/S0002-9947-09-04783-7
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