  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.
