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 language||English (US)|
|Number of pages||9|
|Journal||Pacific Journal of Mathematics|
|State||Published - Dec 1984|