Vitali’s theorem and WWKL

Vitali’s theorem and WWKL

Cached

Download Links

[www.math.psu.edu]

by Douglas K. Brown , Mariagnese Giusto , Stephen G. Simpson

Venue:	Archive for Mathematical Logic
Citations:	1 - 0 self

BibTeX

@ARTICLE{Brown_vitali’stheorem,
    author = {Douglas K. Brown and Mariagnese Giusto and Stephen G. Simpson},
    title = {Vitali’s theorem and WWKL},
    journal = {Archive for Mathematical Logic},
    year = {},
    volume = {41},
    pages = {2002}
}

Bookmark

OpenURL

Abstract

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. 1.

Citations

294	The definition of random sequences - Martin-Löf
46	Constructive analysis, Grundlehren der - Bishop, Bridges - 1985
33	Partial realizations of Hilbert’s program - Simpson - 1988
27	Π 0 1 classes, and complete extensions of - Measure - 1985
12	Which set existence axioms are needed to prove the separable Hahn-Banach theorem?, Annals of Pure and Applied Logic 31 - Brown, Simpson - 1986
10	Functional Analysis in Weak Subsystems of Second Order Arithmetic - Brown - 1987
8	Fragments of arithmetic. Annals of Pure and Applied Logic,28:33-71 - Sieg - 1985
7	Countable Algebra and Set Existence Axioms,” Ann - Friedman, Simpson, et al. - 1983
6	S.G.Simpson, Separable Banach space theory needs strong set existence axioms - Humphreys - 1996
6	of second order arithmetic - Subsystems - 1999
4	Measure theory in weak subsystems of second order arithmetic - Yu - 1987
3	Measure theory and weak König’s lemma, Archive for Mathematical Logic 30 - Yu, Simpson - 1990
2	Remarks on constructive mathematical analysis - Demuth, Kucera - 1979
2	unpublished communication to Leo Harrington - Friedman - 1977
1	to “Countable algebra and set existence axioms”, Annals of Pure and Applied Logic 27 - Addendum - 1985
1	and generalizations of fixed point free functions - Randomness - 1990
1	relative randomness, Annals of Pure and Applied Logic 63 - On - 1993
1	theorem is equivalent to arithmetical comprehension - Radon-Nikodym - 1990
1	representation theorem, Borel measures, and subsystems of second order arithmetic, Annals of Pure and Applied Logic 59 - Riesz - 1993
1	convergence theorems and reverse mathematics, Mathematical Logic Quarterly 40 - Lebesgue - 1994