Vitali's Theorem and WWKL

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Archive for Mathematical Logic 41 (2):191-206 (2002)
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Abstract

Continuing the investigations of X. Yu and others, we study the role of set existence axioms in classical Lebesgue measure theory. We show that pairwise disjoint countable additivity for open sets of reals is provable in RCA0. We show that several well-known measure-theoretic propositions including the Vitali Covering Theorem are equivalent to WWKL over RCA0.

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10.1007/s001530100100

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Citations of this work

Mass problems and randomness.Stephen G. Simpson - 2005 - Bulletin of Symbolic Logic 11 (1):1-27.
A Nonstandard Counterpart of WWKL.Stephen G. Simpson & Keita Yokoyama - 2011 - Notre Dame Journal of Formal Logic 52 (3):229-243.
Almost everywhere domination.Natasha L. Dobrinen & Stephen G. Simpson - 2004 - Journal of Symbolic Logic 69 (3):914-922.
Fundamental notions of analysis in subsystems of second-order arithmetic.Jeremy Avigad - 2006 - Annals of Pure and Applied Logic 139 (1):138-184.

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References found in this work

Subsystems of Second Order Arithmetic.Stephen G. Simpson - 1999 - Studia Logica 77 (1):129-129.
Countable algebra and set existence axioms.Harvey M. Friedman - 1983 - Annals of Pure and Applied Logic 25 (2):141.
Fragments of arithmetic.Wilfried Sieg - 1985 - Annals of Pure and Applied Logic 28 (1):33-71.

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