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On incomparability and related cardinal functions on ultraproducts of Boolean algebras

Saharon Shelah·Otmar Spinas
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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 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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Saharon Shelah, Otmar Spinas. 1999-03-18. On incomparability and related cardinal functions on ultraproducts of Boolean algebras. https://arxiv.org/abs/math/9903116

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