English

Well-Ordered Model Universes

Logic 2018-12-18 v1

Abstract

In this paper we show how to build a model of ZFCZFC such that all its inner models satisfying the Axiom of Choice are well-ordered with respect to inclusion, and that said ordering is of arbitrary height (including possibly OrdOrd high). We do this by iterating κ\kappa-Sacks forcing for ever-increasing κ\kappa, while showing that such forcings do not add any unexpected intermediate inner models.

Keywords

Cite

@article{arxiv.1812.06192,
  title  = {Well-Ordered Model Universes},
  author = {Alon Navon},
  journal= {arXiv preprint arXiv:1812.06192},
  year   = {2018}
}

Comments

41 pages

R2 v1 2026-06-23T06:43:11.939Z