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Uniform almost everywhere domination

Published online by Cambridge University Press:  12 March 2014

Peter Cholak ,
Noam Greenberg  and
Joseph S. Miller
Peter Cholak
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556-5683, USA.E-mail:Peter.Cholak.l@nd.edu
Noam Greenberg
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556-5683, USA.E-mail:erlkoeing@nd.edu
Joseph S. Miller
Affiliation:
Department of Mathematics, University of Connecticut, U-3009, 196 Auditorium Road, Storrs, CT 06269, USA.E-mail:joseph.s.miller@gmail.com
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 3 , September 2006 , pp. 1057 - 1072
Copyright
Copyright © Association for Symbolic Logic 2006

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