The Journal of Symbolic Logic

Research Article

Uniform almost everywhere domination

Peter Cholaka1, Noam Greenberga2 and Joseph S. Millera3

a1 Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556-5683, USA. E-mail: Peter.Cholak.l@nd.edu

a2 Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556-5683, USA. E-mail: erlkoeing@nd.edu

a3 Department of Mathematics, University of Connecticut, U-3009, 196 Auditorium Road, Storrs, CT 06269, USA. E-mail: joseph.s.miller@gmail.com

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 G δ sets. Our constructions essentially settle the reverse mathematical classification of this principle.

(Received January 25 2006)