Applications of another characterization of betaN\N

TL;DR

This paper explores a new characterization of the topological space betaN\N in the aleph_2-Cohen model, linking it to classical results and providing insights into its properties.

Contribution

It introduces a novel characterization of betaN\N in the Cohen model, connecting topological properties with set-theoretic models and simplifying existing results.

Findings

Derived topological results from Steprans' characterization

Connected properties of betaN\N with Cohen model features

Simplified proofs of classical topological theorems

Abstract

Steprans provided a characterization of betaN\N in the aleph_2-Cohen model that is much in the spirit of Parovicenko's characterization of this space under CH. A variety of the topological results established in the Cohen model can be deduced directly from the properties of betaN\N or P(N)/fin that feature in Steprans' result.