PCF arithmetic without and with choice

TL;DR

This paper explores provable variants of the GCH and its rank version under weak choice assumptions, providing new insights even within ZFC.

Contribution

It introduces results on the rank version of the revised GCH under weak choice, expanding understanding of these principles without full AC.

Findings

Results are provable under weak choice assumptions.

Additional information is obtained even within ZFC.

Advances understanding of GCH variants and their provability.

Abstract

We deal with relatives of GCH which are provable. In particular we deal with rank version of the revised GCH. Our motivation was to find such results when only weak versions of the axiom of choice are assumed but some of the results gives us additional information even in ZFC.