When the continuum has cofinality ω1

Arnold W. Miller, Karel Prikry

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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
Issue number2
StatePublished - Dec 1984


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