English

Models of Set Theory: Extensions and Dead-ends

Logic 2026-04-07 v7

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.

Keywords

Cite

@article{arxiv.2406.14790,
  title  = {Models of Set Theory: Extensions and Dead-ends},
  author = {Ali Enayat},
  journal= {arXiv preprint arXiv:2406.14790},
  year   = {2026}
}

Comments

31 pages; some typos have been corrected, the most important of which is that in Theorem C of the abstract, the theory ZFC has been replaced by ZF

R2 v1 2026-06-28T17:14:11.083Z