Journal of Symbolic Logic

Uniform almost everywhere domination

Peter Cholak, Noam Greenberg, and Joseph S. Miller

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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.

Article information

Source
J. Symbolic Logic Volume 71, Issue 3 (2006), 1057-1072.

Dates
First available in Project Euclid: 4 August 2006

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

Citation

Cholak, Peter; Greenberg, Noam; Miller, Joseph S. Uniform almost everywhere domination. J. Symbolic Logic 71 (2006), no. 3, 1057--1072. doi:10.2178/jsl/1154698592. http://projecteuclid.org/euclid.jsl/1154698592.


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