Exact equiconsistency results for Δ 3 1 -sets of reals

Archive for Mathematical Logic 32 (2):101-112 (1992)
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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

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Citations of this work

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Dominating projective sets in the Baire space.Otmar Spinas - 1994 - Annals of Pure and Applied Logic 68 (3):327-342.
Mathias absoluteness and the Ramsey property.Lorenz Halbeisen & Haim Judah - 1996 - Journal of Symbolic Logic 61 (1):177-194.

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References found in this work

Set theory.Thomas Jech - 1981 - Journal of Symbolic Logic.
Happy families.A. R. D. Mathias - 1977 - Annals of Mathematical Logic 12 (1):59.
Internal cohen extensions.D. A. Martin & R. M. Solovay - 1970 - Annals of Mathematical Logic 2 (2):143-178.
Some exact equiconsistency results in set theory.Leo Harrington & Saharon Shelah - 1985 - Notre Dame Journal of Formal Logic 26 (2):178-188.
A new proof that analytic sets are Ramsey.Erik Ellentuck - 1974 - Journal of Symbolic Logic 39 (1):163-165.

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