Iterated forcing and normal ideals on ω 1

Saharon Shelah*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

We prove that suitable iteration does not collapse א1 [and does not add reals], i.e., that in such iteration, certain sealing of maximal antichains of stationary subsets of ω 1 is allowed. As an application, e.g., we prove from supercompact hypotheses, mainly, the consistency of: ZFC + GCH + "for some stationary set S ⊆ω 1, {ie345-1}(ω 1)/(D ω 1 +S) is the Levy algebra" (i.e., the complete Boolean Algebra corresponding to the Levy collapse Levy (א0,<א2) (and we can add "a variant of PFA") and the consistency of the same, with "Ulam property" replacing "Levy algebra"). The paper assumes no specialized knowledge (if you agree to believe in the semi-properness iteration theorem and RCS iteration).

Original languageEnglish
Pages (from-to)345-380
Number of pages36
JournalIsrael Journal of Mathematics
Volume60
Issue number3
DOIs
StatePublished - Dec 1987

Fingerprint

Dive into the research topics of 'Iterated forcing and normal ideals on ω 1'. Together they form a unique fingerprint.

Cite this