2022/02/02 by Brendle, Joerg
#03E05 #03E17 #03E35 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2202.00897
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.