### On incomparability and related cardinal functions on ultraproducts of Boolean algebras

by Shelah and Spinas. [ShSi:677]

Math Japonica, 2000

Let C denote any of the following cardinal
characteristics of Boolean algebras: incomparability, spread,
character, pi-character, hereditary Lindel{o}f number, hereditary
density. It is shown to be consistent that there
exists a sequence < B_i:i< kappa > of Boolean
algebras and an ultrafilter D on kappa such that
C(prod_{i< kappa}B_i/D)<| prod_{i< kappa}C(B_i)/D| . This
answers a number of problems posed by Monk.

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