Large Cardinal Axioms from Tameness in AECs

TL;DR

This paper demonstrates that certain tameness properties in abstract elementary classes imply the existence of large cardinals, linking model theory with set-theoretic large cardinal hypotheses.

Contribution

It establishes a novel connection between tameness in AECs and large cardinal axioms, under mild cardinal arithmetic assumptions.

Findings

Tameness assertions imply large cardinal existence.

Results depend on mild cardinal arithmetic assumptions.

Bridges between model theory and set theory are developed.

Abstract

We show that various tameness assertions about abstract elementary classes imply the existence of large cardinals under mild cardinal arithmetic assumptions.