Uniform almost everywhere domination

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 prooftheoretic strength of the regularity of Lebesgue measure for G sets. Our constructions essentially settle the reverse mathematical classification of this principle.

• Type: Journal
• Year: 2006
• Where: JSYML
• Authors: Peter Cholak, Noam Greenberg, Joseph S. Miller
• Keywords: Forcing Construction, JSYML 2006, Lebesgue Measure, Priority Construction