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Mass Problems and Measure-Theoretic Regularity

  • Stephen G. Simpson (a1)
Abstract

A well known fact is that every Lebesgue measurable set is regular, i.e., it includes an F σ set of the same measure. We analyze this fact from a metamathematical or foundational standpoint. We study a family of Muchnik degrees corresponding to measuretheoretic regularity at all levels of the effective Borel hierarchy. We prove some new results concerning Nies's notion of LR-reducibility. We build some ω-models of RCA0 which are relevant for the reverse mathematics of measure-theoretic regularity.

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Bulletin of Symbolic Logic
  • ISSN: 1079-8986
  • EISSN: 1943-5894
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