Lower bounds of sets of P-points

TL;DR

This paper demonstrates that under Martin's Axiom, collections of P-c points with certain upper bounds also have corresponding lower bounds, revealing new structural properties of P-points in set theory.

Contribution

It establishes a new lower bound property for P-points under Martin's Axiom, extending understanding of their structural relationships.

Findings

Under MA_kappa, collections of P_c-points with an RK upper bound also have an RK lower bound.

The result links the existence of upper bounds to the existence of lower bounds for P-points.

Provides insights into the structure of P-points in the context of set-theoretic axioms.

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.