Nice aleph_1 generated non-P-points, I

TL;DR

This paper introduces a new family of ultrafilters on natural numbers that are distinct from P-points, demonstrating their possible existence independently of P-points under certain conditions.

Contribution

It defines and proves the existence of ultrafilters that are far from P-points, expanding understanding of ultrafilter diversity.

Findings

Existence of non-P-point ultrafilters under reasonable conditions

Construction of ultrafilters far from P-points

Potential independence from P-points in set theory

Abstract

We define a family of a (non-principal) ultrafilters on N which are, in a sense, far from P-points. We first under reasonable conditions, prove its existence. In a continuation we shall prove that such a point may exist while no P-point exists.