Homogeneity of the Lévy collapse from the perspective of Fraïssé theory

Abstract

Given a strongly inaccessible cardinal $\lambda$, we study the Fraïssé class of all Boolean algebras of size $<\lambda$, together with regular embeddings. We prove that this is indeed a Fraïsséclass, and its limit has the same completion as the Lévy collapse. We also give a direct proof that the collapsing algebra of density $\kappa$ is not the union of a $\kappa$-chain of regular sub-algebras of density $<\kappa$.