English

On double-membership graphs of models of Anti-Foundation

Logic 2025-03-14 v1

Abstract

We answer some questions about graphs which are reducts of countable models of Anti-Foundation, obtained by considering the binary relation of double-membership xyxx\in y\in x. We show that there are continuum-many such graphs, and study their connected components. We describe their complete theories and prove that each has continuum-many countable models, some of which are not reducts of models of Anti-Foundation.

Keywords

Cite

@article{arxiv.1908.02708,
  title  = {On double-membership graphs of models of Anti-Foundation},
  author = {Bea Adam-Day and John Howe and Rosario Mennuni},
  journal= {arXiv preprint arXiv:1908.02708},
  year   = {2025}
}

Comments

15 pages, 2 figures