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Journal Article
Base matrices of various heights
2023
Overview
A classical theorem of Balcar, Pelant, and Simon says that there is a base matrix of height
${\\mathfrak h}$
, where
${\\mathfrak h}$
is the distributivity number of
${\\cal P} (\\omega ) / {\\mathrm {fin}}$
. We show that if the continuum
${\\mathfrak c}$
is regular, then there is a base matrix of height
${\\mathfrak c}$
, and that there are base matrices of any regular uncountable height
$\\leq {\\mathfrak c}$
in the Cohen and random models. This answers questions of Fischer, Koelbing, and Wohofsky.
Publisher
Canadian Mathematical Society,Cambridge University Press
Subject
