Measure-Theoretic Uniformity in Recursion Theory and Set Theory
نویسندگان
چکیده
منابع مشابه
Uniformity, Universality, and Recursion Theory
We prove a number of results motivated by global questions of uniformity in recursion theory, and some longstanding open questions about universality of countable Borel equivalence relations. Our main technical tool is a class of games for constructing functions on free products of countable groups. These games show the existence of refinements of Martin’s ultrafilter on Turing invariant sets t...
متن کاملMeasure-theoretic Uniformity
Here we present the principal ideas and results of [5] with some indications of proof. We introduce the notion of measure-theoretic uniformity, and we describe its use in recursion theory, hyperarithmetic analysis, and set theory. In recursion theory we show that the set of all sets T such that the ordinals recursive in T are the recursive ordinals has measure 1. In set theory we obtain all of ...
متن کاملSome Remarks on Set Theory, Ix . Combinatorial Problems in Measure Theory and Set Theory
Now, in analogy to Ramsay's theorem, one might consider the following problem. Suppose that, for some u > 0, there is associated with each k-tuple X = {x l , • • • , xk } of elements of an infinite set S a measurable set F(X) of [0, 1] such that m(F(X)) > u . Does there always exist an infinite subset S' of S such that the sets F(X) corresponding to the k-tuples X of S' have a nonempty intersec...
متن کاملMeasurement-Theoretic Frameworks for Fuzzy Set Theory
Two different but related measurement problems are considered within the fuzzy set theory. The first problem is the membership measurement and the second is property ranking. These two measurement problems are combined and two axiomatizations of fuzzy set theory are obtained. In the first one, the indifference is transitive but in the second one this drawback is removed by utilizing interval or...
متن کاملThe Uniform Regular Set Theorem in a-Recursion Theory
Several new features arise in the generalization of recursion theory on crl to recursion theory on admissible ordinals d, thus making ¿y-recursion theory an interesting theory. One of these is the appearance of irregular sets. A subset A of a is called regular (over a), if we have for all B<a that AnBeL-, otherwise A is called irregular (over ø). So in the special case of ordinary recursion the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1969
ISSN: 0002-9947
DOI: 10.2307/1995364