Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-12-03T19:13:22.207Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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