English

Counting siblings in universal theories

Logic 2022-09-14 v3

Abstract

We show that if a countable structure MM in a finite relational language is not cellular, then there is an age-preserving NMN \supseteq M such that 202^{\aleph_0} many structures are bi-embeddable with NN. The proof proceeds by a case division based on mutual algebraicity.

Keywords

Cite

@article{arxiv.1910.11230,
  title  = {Counting siblings in universal theories},
  author = {Samuel Braunfeld and Michael C. Laskowski},
  journal= {arXiv preprint arXiv:1910.11230},
  year   = {2022}
}

Comments

26 pages; v3 to appear in Journal of Symbolic Logic

R2 v1 2026-06-23T11:53:56.103Z