Randomness in effective descriptive set theory
نویسندگان
چکیده
An analog of ML-randomness in the effective descriptive set theory setting is studied, where the r.e. objects are replaced by their Π1 counterparts. We prove the analogs of the Kraft-Chaitin Theorem and Schnorr’s Theorem. In the new setting, while K-trivial sets exist that are not hyper-arithmetical, each low for random set is. Finally we study a very strong yet effective randomness notion: Z is strongly random if Z is in no null Π1 set of reals. We show that there is a greatest Π1 null set, that is, a universal test for this notion.
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D ec 2 01 6 RANDOMNESS VIA INFINITE COMPUTATION AND EFFECTIVE DESCRIPTIVE SET THEORY
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My primary research interest is in computability and complexity theory. More specifically, I have an active research program in the area of effective dimension theory and randomness. Computability theory was first developed in the 1930s and ’40s by Alan Turing who has come to be seen, along with Gödel and Tarski, as one one of the founders of modern mathematical logic. The subject developed ove...
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