Uniform almost everywhere domination
逻辑
2007-05-23 v2
摘要
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 sets. Our constructions essentially settle the reverse mathematical classification of this principle. Revised Nov 13, 2005. Minor corrections made.
引用
@article{arxiv.math/0506019,
title = {Uniform almost everywhere domination},
author = {Peter Cholak and Joseph Miller and Noam Greenberg},
journal= {arXiv preprint arXiv:math/0506019},
year = {2007}
}