Monoidal Symmetric Models

TL;DR

This paper introduces a novel approach to interpreting large cardinal axioms through topological symmetries, enabling the construction of symmetric inner models and resolving longstanding set theory problems.

Contribution

It presents a new method linking large cardinal axioms with topological symmetries, leading to symmetric inner models and new proofs of key set theory results.

Findings

Derived a symmetric inner model construction.

Proved the Kunen inconsistency using stabiliser arguments.

Resolved an open problem of Rogers.

Abstract

We develop a new method of interpreting large cardinal axioms as giving rise to topological symmetries of the universe of sets, similar to the construction of Fraenkel-Mostowski-Specker models. This allows us to define a "symmetric" inner model construction. In this vein, we use Fraenkel-Mostowski-Specker type stabiliser arguments to deduce the Kunen inconsistency, as well as resolving an open problem of Rogers.