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Exact equiconsistency results for Δ 3 1 -sets of reals

Exact equiconsistency results for Δ 3 1 -sets of reals We improve a theorem of Raisonnier by showing that Cons(ZFC+every Σ 2 1 -set of reals in Lebesgue measurable+every Π 2 1 -set of reals isK σ-regular) implies Cons(ZFC+there exists an inaccessible cardinal). We construct, fromL, a model where every Δ 3 1 -sets of reals is Lebesgue measurable, has the property of Baire, and every Σ 2 1 -set of reals isK σ-regular. We prove that if there exists a Σ n+1 1 unbounded filter on ω, then there exists a nonK σ-regular Π 2 1 -subset. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

Exact equiconsistency results for Δ 3 1 -sets of reals

Archive for Mathematical Logic , Volume 32 (2) – Feb 21, 2005

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References (17)

Publisher
Springer Journals
Copyright
Copyright © 1992 by Springer-Verlag
Subject
Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/BF01269952
Publisher site
See Article on Publisher Site

Abstract

We improve a theorem of Raisonnier by showing that Cons(ZFC+every Σ 2 1 -set of reals in Lebesgue measurable+every Π 2 1 -set of reals isK σ-regular) implies Cons(ZFC+there exists an inaccessible cardinal). We construct, fromL, a model where every Δ 3 1 -sets of reals is Lebesgue measurable, has the property of Baire, and every Σ 2 1 -set of reals isK σ-regular. We prove that if there exists a Σ n+1 1 unbounded filter on ω, then there exists a nonK σ-regular Π 2 1 -subset.

Journal

Archive for Mathematical LogicSpringer Journals

Published: Feb 21, 2005

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