Journal of Symbolic Logic

Uniform almost everywhere domination

Peter Cholak,Noam Greenberg, and Joseph S. Miller

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

First available: 4 August 2006

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

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