Ultrafilters in the random real model

TL;DR

This paper demonstrates the existence of P-points and Gruff ultrafilters in certain forcing extensions with fewer than leph_{} leph_{} random reals, refining previous results in set theory.

Contribution

It establishes the existence of P-points and Gruff ultrafilters in models extended by adding fewer than leph_{} random reals, correcting earlier theorems.

Findings

P-points and Gruff ultrafilters exist in these models.

Results hold in extensions with fewer than leph_{} random reals.

Improves and corrects previous literature on ultrafilters in forcing extensions.

Abstract

We prove that \textsf{P}-points (even strong P-points) and Gruff ultrafilters exist in any forcing extension obtained by adding fewer than $\aleph_{\omega}% $-many random reals to a model of \textsf{CH. }These results improve and correct previous theorems that can be found in the literature.