, Volume 20, Issue 2, pp 149-163

A model of ZF with an infinite free complete Boolean algebra

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Abstract

By a theorem of Gaifman and Hales no model of ZF+AC (Zermelo-Fraenkel set theory plus the axiom of choice) contains an infinite free complete Boolean algebra. We construct a model of ZF in which an infinite free c.B.a. exists.

Preparation of this paper was partially supported by NSF Grant No. 43901.