No random reals in countable support iterations
We prove a preservation theorem for limit steps of countable support iterations of proper forcing notions whose particular cases are preservations of the following properties on limit steps: “no random reals are added”, “μ(Random(V))≠1”, “no dominating reals are added”, “Cohen(V) is not comeager”. Consequently, countable support iterations of σ-centered forcing notions do not add random reals.
KeywordsInverse Limit Random Real Force Notion Baire Space Majorant Series
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- T. Bartoszynski and H. Judah,Measure and Category, in preparation.Google Scholar
- M. Goldstern,Forcing tools for your forcing construction, inSet Theory of the Reals 1991 (H. Judah, ed.), Israel Mathematical Conference Proceeding6 (1993), 305–360.Google Scholar
- T. Jech,Set Theory, Academic Press, New York, 1978.Google Scholar
- S. Shelah,Proper and Improper Forcing, to appear.Google Scholar
- J. Stern,Generic extensions which do not add random reals, Proc. Caracas, Lecture Notes in Mathematics1130, Springer-Verlag, Berlin, 1983, pp. 395–407.Google Scholar