A note on the Revised GCH

TL;DR

This paper simplifies the proof of a key theorem by removing the need for large cardinal assumptions, using only well-foundedness of reduced products of ordinals.

Contribution

It provides a new proof of Theorem 2.10 that avoids Shelah's filters and large cardinal assumptions, relying solely on well-foundedness.

Findings

Eliminates Shelah's nice filters from the proof

Removes assumptions about large cardinals in core models

Uses well-foundedness of reduced products of ordinals

Abstract

We give a proof of Theorem 2.10 from [8] that eliminates the use of Shelah's nice filters and associated rank functions, and instead uses only the well-foundedness of reduced products of ordinals modulo countably complete filters. This removes any need to make assumptions about the existence of large cardinals in core models.