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Base matrices of various heights
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 66 / Issue 4 / December 2023
- Published online by Cambridge University Press:
- 20 April 2023, pp. 1237-1243
- Print publication:
- December 2023
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- Article
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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.
