Base matrices of various heights

Brendle, Jörg 

Canadian mathematical bulletin, Tome 66 (2023) no. 4, pp. 1237-1243

Résumé

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.

Détail

DOI : 10.4153/S0008439523000310

Mots-clés : Base matrix, refining matrix, distributivity number, splitting number