RANDOMNESS NOTIONS AND REVERSE MATHEMATICS

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Reverse Mathematics, Mass Problems, and Effective Randomness

1 reverse mathematics z z z z z z z z z z z z z z z z z z z z z z z z z z z z z z z z z z z z z z z z z z z z z z z z z z mass problems effective randomness Foundations of mathematics is the study of the most basic concepts and logical structure of mathematics as a whole. Reverse mathematics is a particular research program in the foundations of mathematics. The goal of reverse mathematics is t...

متن کامل

Algorithmic randomness, reverse mathematics, and the dominated convergence theorem

We analyze the pointwise convergence of a sequence of computable elements of L(2) in terms of algorithmic randomness. We consider two ways of expressing the dominated convergence theorem and show that, over the base theory RCA0, each is equivalent to the assertion that every Gδ subset of Cantor space with positive measure has an element. This last statement is, in turn, equivalent to weak weak ...

متن کامل

Comparing notions of randomness

It is an open problem in the area of computable randomness whether Kolmogorov-Loveland randomness coincides with Martin-Löf randomness. Joe Miller and André Nies suggested some variations of Kolmogorov-Loveland randomness to approach this problem and to provide a partial solution. We show that their proposed notion of partial permutation randomness is still weaker than Martin-Löf randomness.

متن کامل

Randomness notions and partial relativization

We study weak 2 randomness, weak randomness relative to ∅′ and Schnorr randomness relative to ∅′. One major theme is characterizing the oracles A such that ML[A] ⊆ C, where C is a randomness notion and ML[A] denotes the Martin-Löf random reals relative to A. We discuss the connections with LR-reducibility and also study the reducibility associated with weak 2randomness.

متن کامل

Complexity of Randomness Notions

Schnorr famously proved that Martin-Löf-randomness of a sequence A can be characterised via the complexity of A’s initial segments. Nies, Stephan and Terwijn as well as independently Miller showed that Kolmogorov randomness coincides with Martin-Löf randomness relative to the halting problem K; that is, a set A is Martin-Löf random relative to K iff there is no function f such that for all m an...

متن کامل

ذخیره 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: The Journal of Symbolic Logic

سال: 2019

ISSN: 0022-4812,1943-5886

DOI: 10.1017/jsl.2019.50