Covering with Chang models over derived models

TL;DR

This paper introduces a covering conjecture related to superstrong cardinals, proves its validity in hod mice, and revises a previous conjecture involving universally Baire functions, advancing the understanding of inner model theory.

Contribution

It formulates a new covering conjecture below superstrong cardinals and proves it within hod mice, refining earlier conjectures involving universally Baire functions.

Findings

The covering conjecture holds in hod mice.

The conjecture is expected to be true below superstrong cardinals.

It revises the UB Covering Conjecture from previous work.

Abstract

We present a covering conjecture that we expect to be true below superstrong cardinals. We then show that the conjecture is true in hod mice. This work is a continuation of the work that started in Covering with Universally Baire Functions Advances in Mathematics, and the main conjecture of the current paper is a revision of the UB Covering Conjecture of the aforementioned paper.