Baumgartner's axiom

Baumgartner's axiom, often denoted as \( \mathsf{BA} \), is a principle in set theory proposed by the mathematician J. D. Baumgartner. It provides a framework for working with elementary embeddings and large cardinals. Specifically, Baumgartner's axiom asserts the existence of certain types of elementary embeddings, particularly those that are related to the structure of the set-theoretic universe in the presence of large cardinals.