On incomparability and related cardinal functions on ultraproducts of Boolean algebras
Abstract
Let C denote any of the following cardinal characteristics of Boolean algebras: incomparability, spread, character, pi-character, hereditary Lindelof number, hereditary density. It is shown to be consistent that there exists a sequence <Bi:i<kappa> of Boolean algebras and an ultrafilter D on kappa such that C(prodi<kappaBi/D)<|prodi<kappaC(Bi)/D|. This answers a number of problems posed by Monk.
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