Uniform Almost Everywhere Domination

Journal of Symbolic Logic 71 (3):1057 - 1072 (2006)
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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

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Citations of this work

Almost Everywhere Domination and Superhighness.Stephen G. Simpson - 2007 - Mathematical Logic Quarterly 53 (4):462-482.
Mass Problems and Hyperarithmeticity.Joshua A. Cole & Stephen G. Simpson - 2007 - Journal of Mathematical Logic 7 (2):125-143.
Van Lambalgen's Theorem and High Degrees.Johanna N. Y. Franklin & Frank Stephan - 2011 - Notre Dame Journal of Formal Logic 52 (2):173-185.
Tracing and Domination in the Turing Degrees.George Barmpalias - 2012 - Annals of Pure and Applied Logic 163 (5):500-505.

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