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Why Solovay real produces Cohen real

Published online by Cambridge University Press:  12 March 2014

Janusz Pawlikowski
Janusz Pawlikowski*
Affiliation:
Mathematical Institute, University of Wrocław, Wrocław, Poland
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Abstract

An explanation is given of why, after adding to a model M of ZFC first a Solovay real r and next a Cohen real c, in M[r] [c] a Cohen real over M[c] is produced. It is also shown that a Solovay algebra iterated with a Cohen algebra can be embedded into a Cohen algebra iterated with a Solovay algebra.

Keywords

Cohen realSolovay realmeasurecategorycardinal indices
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 51 , Issue 4 , December 1986 , pp. 957 - 968
Copyright
Copyright © Association for Symbolic Logic 1986

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References

REFERENCES

[B]Bartoszyński, T., Additivity of measure implies additivity of category, Transactions of the American Mathematical Society, vol. 281 (1984), pp. 209–213.CrossRefGoogle Scholar
[B1]Bartoszyński, T., Combinatorial aspects of measure and category, Fundamenta Mathematicae (to appear).Google Scholar
[Bu]Bukovský, L., Random forcing, Set theory and hierarchy theory. V (Bierutowice, 1976; Lachlan, A.et al., editors), Lecture Notes in Mathematics, vol. 619, Springer-Verlag, Berlin, 1977, pp. 101–117.CrossRefGoogle Scholar
[CP]Cichoń, J. and Pawlikowski, J., On ideals of subsets of the plane and on Cohen reals, this Journal, vol. 51 (1986), pp. 560–569.Google Scholar
[F]Fremlin, D. H., Cichoń's diagram, Séminaire d'initiation à l'analyse, 61 (Choquet, G.et al., editors), Publications Mathématiques de l'Universite Pierre et Marie Curie, Paris, 1985.Google Scholar
[K]Kechris, A. S., Measure and category in effective descriptive set theory, Annals of Mathematical Logic, vol. 5 (1973), pp. 337–384.CrossRefGoogle Scholar
[Kr]Krawczyk, A., A note on random reals, handwritten note, 1983.Google Scholar
[M]Miller, A. W., Some properties of measure and category, Transactions of the American Mathematical Society, vol. 266 (1981), pp. 93–114.CrossRefGoogle Scholar
[M1]Miller, A. W., Corrections and additions to [M], Transactions of the American Mathematical Society, vol. 271 (1982), pp. 347–348.Google Scholar
[P]Pawlikowski, J., Lebesgue measurability implies Baire property, Bulletin des Sciences Mathematiques, vol. 109 (1985), pp. 321–324.Google Scholar
[RS]Raisonnier, J. and Stern, J., The strength of measurability hypotheses, Israel Journal of Mathematics, vol. 50 (1985), pp. 337–349.CrossRefGoogle Scholar
[S]Solovay, R. M., A model of set theory in which every set is Lebesgue measurable, Annals of Mathematics, ser. 2, vol. 92 (1970), pp. 1–56.CrossRefGoogle Scholar
[T]Truss, J., Sets having calibre ℵ1, Logic Colloquium '76 (Gandy, R. O. and Hyland, J. M. E., editors), North-Holland, Amsterdam, 1977, pp. 595–612.Google Scholar
[T1]Truss, J., The noncommutativity of random and generic extensions, this Journal, vol. 48 (1983), pp. 1008–1012.Google Scholar