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|Title:||A π1 1-uniformization principle for reals|
|Authors:||Chong, C.T. |
|Source:||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|
|Appears in Collections:||Staff Publications|
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