`Ultrafilters Relaxed' -- Species of Families of Subsets

TL;DR

This paper explores various 'species' of families of subsets, examining their properties and potential as relaxed alternatives to ultrafilters in logic and limit processes.

Contribution

It introduces and analyzes new classes of subset families, expanding the understanding of ultrafilter-like structures in set theory.

Findings

Identifies properties of 'species' of families of subsets.

Establishes parallels between these families and ultrafilters.

Suggests potential applications in logic and limit processes.

Abstract

An assortments of `species' of families of subsets of a set and some of their properties are investigated, with an eye on the logic and limit role they may play as `relaxed parallels' to ultrafilters.