Lower bounds of sets of P-points

Abstract

We show that ${\mathrm{MA}}_{\kappa }$ implies that each collection of $P_{\mathfrak{c}}$-points of size at most $\kappa$ which has a $P_{\mathfrak{c}}$-point as an $RK$ upper bound also has a $P_{\mathfrak{c}}$-point as an $RK$ lower bound.