On ultraproducts of Boolean Algebras and irr
Abstract
We prove the consistency of irr(prod limitsi<kappaBi/D)< prod limitsi<kappairr(Bi)/D, where D is an ultrafilter on kappa and each Bi is a Boolean Algebra. This solves the last problem of this form from the Monk's list of problems, that is number 35. The solution applies to many other properties, e.g., Souslinity. Next, we get similar results with kappa = aleph1 (easily we cannot have it for kappa=aleph0) and Boolean Algebras Bi (i< kappa) of cardinality < bethomega1.
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