### Uniform almost everywhere domination

Peter Cholak, Noam Greenberg, and Joseph S. Miller
Source: J. Symbolic Logic Volume 71, Issue 3 (2006), 1057-1072.

#### Abstract

We explore the interaction between Lebesgue measure and dominating functions. We show, via both a priority construction and a forcing construction, that there is a function of incomplete degree that dominates almost all degrees. This answers a question of Dobrinen and Simpson, who showed that such functions are related to the proof-theoretic strength of the regularity of Lebesgue measure for Gδ sets. Our constructions essentially settle the reverse mathematical classification of this principle.

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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1154698592
Digital Object Identifier: doi:10.2178/jsl/1154698592
Mathematical Reviews number (MathSciNet): MR2251556
Zentralblatt MATH identifier: 1109.03034

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