## Journal of Symbolic Logic

- J. Symbolic Logic
- Volume 69, Issue 3 (2004), 914-922.

### Almost everywhere domination

Natasha L. Dobrinen and Stephen G. Simpson

#### Abstract

A Turing degree **a** is said to be *almost
everywhere dominating* if, for almost all X∈ 2^{ω} with respect
to the “fair coin” probability measure on 2^{ω}, and for all
g : ω→ω Turing reducible to X, there exists
f : ω→ω of Turing degree **a** which
dominates g. We study the problem of characterizing the almost
everywhere dominating Turing degrees and other, similarly defined
classes of Turing degrees. We relate this problem to some questions
in the reverse mathematics of measure theory.

#### Article information

**Source**

J. Symbolic Logic, Volume 69, Issue 3 (2004), 914-922.

**Dates**

First available in Project Euclid: 4 October 2004

**Permanent link to this document**

https://projecteuclid.org/euclid.jsl/1096901775

**Digital Object Identifier**

doi:10.2178/jsl/1096901775

**Mathematical Reviews number (MathSciNet)**

MR2078930

**Zentralblatt MATH identifier**

1075.03021

#### Citation

Dobrinen, Natasha L.; Simpson, Stephen G. Almost everywhere domination. J. Symbolic Logic 69 (2004), no. 3, 914--922. doi:10.2178/jsl/1096901775. https://projecteuclid.org/euclid.jsl/1096901775