Vaught's conjecture for theories of discretely ordered structures

Abstract

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

References in corpus (1)

• Stationarily ordered types and the number of countable models