Suslin cardinals and cutpoints in mouse limits

TL;DR

This paper investigates the relationship between Suslin cardinals and cutpoints within the framework of mouse limits, providing partial results towards a broader conjecture in inner model theory.

Contribution

It offers a partial proof connecting Suslin cardinals and cutpoints in the context of projectum stable mouse pairs, advancing understanding in inner model theory.

Findings

Established one direction of the Suslin cardinal and cutpoint equivalence

Provided partial results supporting the conjecture in specific cases

Enhanced understanding of the structure of mouse limits in set theory

Abstract

We obtain a partial result on the following conjecture. Conjecture. Let (P, {\Sigma}) be a projectum stable mouse pair, and let \kappa be a cardinal of V such that \kappa < o(M_\infty(P, {\Sigma})); then the following are equivalent: (1) \kappa is a Suslin cardinal, (2) \kappa is a cutpoint of M_\infty(P, {\Sigma}).