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Generalization of one construction by Solovay

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Abstract

The well-known Σ-construction in forcing by Solovay is generalized to the case of intermediate sets that are not subsets of the initial model. Our method gives a more transparent construction of a forcing over an intermediate model than that in the classical paper [1] by Grigorieff on intermediate models.

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References

  1. Grigorieff S., “Intermediate submodels and generic extensions of set theory,” Ann. Math., 101, 447–490 (1975).

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  2. Solovay R. M., “A model of set theory in which every set of reals is Lebesgue measurable,” Ann. Math., 92, 1–56 (1970).

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  3. Kanovei V. G. and Lyubetsky V. A., Modern Set Theory: Borel and Projective Sets [in Russian], MTsNMO, Moscow (2013).

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  4. Kanovei V. G. and Lyubetsky V. A., “An effective minimal encoding of uncountable sets,” Siberian Math. J., 52, No. 5, 854–863 (2011).

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  5. Kanovei V., Borel Equivalence Relations: Structure and Classification, Amer. Math. Soc., New York (2008) (Univ. Lect. Ser. Amer. Math. Soc.; V. 44).

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Correspondence to V. G. Kanovei.

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Original Russian Text Copyright © 2015 Kanovei V.G. and Lyubetsky V.A.

Moscow. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 6, pp. 1341–1350, November–December, 2015; DOI: 10.17377/smzh.2015.56.611.

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Kanovei, V.G., Lyubetsky, V.A. Generalization of one construction by Solovay. Sib Math J 56, 1072–1079 (2015). https://doi.org/10.1134/S0037446615060117

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  • DOI: https://doi.org/10.1134/S0037446615060117

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