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arXiv · 2202.00897

Base matrices of various heights

Joerg Brendle
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Abstract

A classical theorem of Balcar, Pelant, and Simon says that there is a base matrix of height h, where h is the distributivity number of P(omega)/fin. We show that if the continuum c is regular, then there is a base matrix of height c, and that there are base matrices of any regular uncountable height less or equal than c in the Cohen and random models. This answers questions of Fischer, Koelbing, and Wohofsky.

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Joerg Brendle. 2022-02-02. Base matrices of various heights. https://arxiv.org/abs/2202.00897

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