Models of Set Theory: Extensions and Dead-ends (2406.14790v5)

Abstract: This paper is a contribution to the study of extensions of arbitrary models of ZF (Zermelo-Fraenkel set theory), with no regard to countability or well-foundedness of the models involved. We present some new constructions of certain types of extensions, and also establish the existence of models of ZF that cannot be properly end extended to a model of ZF.