English

Vaught's conjecture for theories of discretely ordered structures

Logic 2026-02-24 v3

Abstract

Let TT be a countable complete first-order theory with a definable, infinite, discrete linear order. We prove that TT has continuum-many countable models. The proof is purely first-order, but raises the question of Borel completeness of TT.

Keywords

Cite

@article{arxiv.2212.13605,
  title  = {Vaught's conjecture for theories of discretely ordered structures},
  author = {Predrag Tanović},
  journal= {arXiv preprint arXiv:2212.13605},
  year   = {2026}
}