A Π1-uniformization Principle for Reals
نویسندگان
چکیده
We introduce a Π1-uniformization principle and establish its equivalence with the set-theoretic hypothesis (ω1) = ω1. This principle is then applied to derive the equivalence, to suitable set-theoretic hypotheses, of the existence of Π1 maximal chains and thin maximal antichains in the Turing degrees. We also use the Π1-uniformization principle to study Martin’s conjecture on cones of Turing degrees, and show that under V = L the conjecture fails for uniformly degree invariant Π1 functions.
منابع مشابه
Π1-uniformization Principle for Reals
We introduce a Π1-uniformization principle and establish its equivalence with the set-theoretic hypothesis (ω1) = ω1. This principle is then applied to derive the equivalence, to suitable set-theoretic hypotheses, of the existence of Π1 maximal chains and thin maximal antichains in the Turing degrees. We also use the Π1-uniformization principle to study Martin’s conjectures on cones of Turing d...
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