Abstract
Several people have independently been studying Boolean ultrapowers recently; see for example [2], [3], [4], [6]. Boolean ultrapowers are a quite natural generalization of the well-known usual ultrapowers, but it seemed to be unknown whether every Boolean ultrapower is isomorphic to an ultrapower. We give a negative answer to that question. We further show that a Boolean ultrapower by an ℵ1-regular ultrafilter need not be ℵ2-universal, i.e. that Theorem 4.3.12 of [1] does not hold for Boolean ultrapowers.Let B be a complete Boolean algebra (we identify the algebra with its underlying set), whose operations are denoted by +, ·, −, 0, 1, Σ, Π Let be a structure for some language ℒ. For those who are familiar with Boolean-valued models of set theory, the B-valued model may be described by its underlying setandif R is an n-place relation in ℒ or equality, its interpretation in , u1 … un Є M(B).
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