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Exact equiconsistency results for Δ 13 -sets of reals

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We improve a theorem of Raisonnier by showing that Cons(ZFC+every Σ 12 -set of reals in Lebesgue measurable+every Π 12 -set of reals isK σ-regular) implies Cons(ZFC+there exists an inaccessible cardinal). We construct, fromL, a model where every Δ 13 -sets of reals is Lebesgue measurable, has the property of Baire, and every Σ 12 -set of reals isK σ-regular. We prove that if there exists a Σ 1 n+1 unbounded filter on ω, then there exists a nonK σ-regular Π 12 -subset.

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Authors and Affiliations

  1. Department of Mathematics, Bar-Ilan University, 52900, Ramat-Gan, Israel

    Haim Judah

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  1. Haim Judah
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The author would like to thank the Basic Research Foundation (Israel Academy of Science) for partially supporting this research

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Judah, H. Exact equiconsistency results for Δ 13 -sets of reals. Arch Math Logic 32, 101–112 (1992). https://doi.org/10.1007/BF01269952

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  • DOI: https://doi.org/10.1007/BF01269952

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