On P-like ideals induced by disjoint families

TL;DR

This paper investigates a specific combinatorial property in ideal convergence called the P-property, focusing on ideals induced by disjoint families and identifying conditions under which these ideals possess this property.

Contribution

It characterizes when ideals induced by disjoint families satisfy the P-property and provides necessary coloring-like conditions for selector ideals.

Findings

Not all pairs of ideals induced by disjoint families satisfy the P-property.

Specific inducing partitions determine whether the ideals have the P-property.

A necessary coloring-like condition is established for selector ideals.

Abstract

We consider a combinatorial property isolated in the field of ideal convergence, a P-property for two ideals on natural numbers. We show that among selected ideals induced by disjoint families, not all pairs satisfy P-property for two ideals. In many cases we specify the inducing partitions for which the corresponding ideals possess the property. Regarding selector ideals, a useful coloring-like necessary condition is provided.