The iterability hierarchy above I3

TL;DR

This paper introduces a new hierarchy of large cardinals called the iterability hierarchy, positioned between I3 and I2, and demonstrates that each level implies all the levels below it.

Contribution

It establishes a novel hierarchy of large cardinals and proves the strong implications between its levels, advancing understanding of their relative strength.

Findings

Each step of the hierarchy implies all below it.

The hierarchy fills a gap between I3 and I2.

It provides new insights into the structure of large cardinals.

Abstract

In this paper we introduce a new hierarchy of large cardinals between I3 and I2, the iterability hierarchy, and we prove that every step of it strongly implies the ones below.