When the continuum has cofinality ω1

Arnold W. Miller, Karel Prikry

Research output: Contribution to journalArticle

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Abstract

In this paper we consider models of set theory in which the continuum has cofinality ω1 We show that it is consistent with CH that for any complete boolean algebra B of cardinality less than or equal to c (continuum) there exists an ω1-generated ideal J in P(ω) (power set of ω) such that B is isomorphic to P(ω)mod J. We also show that the existence of generalized Luzin sets for every ω1-saturated ideal in the Borel sets does not imply Martin’s axiom.

Original languageEnglish (US)
Pages (from-to)399-407
Number of pages9
JournalPacific Journal of Mathematics
Volume115
Issue number2
DOIs
StatePublished - Dec 1984

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