Journal of Symbolic Logic

The importance of Π⁰₁ classes in effective randomness

George Barmpalias, Andrew E.M. Lewis, and Keng Meng Ng

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We prove a number of results in effective randomness, using methods in which Π⁰₁ classes play an essential role. The results proved include the fact that every PA Turing degree is the join of two random Turing degrees, and the existence of a minimal pair of LR degrees below the LR degree of the halting problem.

Article information

J. Symbolic Logic, Volume 75, Issue 1 (2010), 387-400.

First available in Project Euclid: 25 January 2010

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Π⁰₁ classes Martin-Löf randomness Peano Arithmetic K-trivials Turing degrees LR degrees


Barmpalias, George; Lewis, Andrew E.M.; Ng, Keng Meng. The importance of Π⁰₁ classes in effective randomness. J. Symbolic Logic 75 (2010), no. 1, 387--400. doi:10.2178/jsl/1264433928.

Export citation