Generic Existence of Independent Families

TL;DR

This paper explores the generic existence of various independent families, extending ultrafilter existence results to p-point, q, and selective independent families, thereby advancing the understanding of their foundational properties.

Contribution

It introduces a generic existence framework for independent families that parallels known ultrafilter results, providing new insights into their structural properties.

Findings

Established generic existence for p-point independent families

Extended results to q and selective independent families

Enhanced understanding of the foundational aspects of independent families

Abstract

We apply the concept of generic existence to p-point, q, and selective independent families that complements and emulates the ultrafilter generic existence results from Canjar and Ketonen.