e/Vaught conjecture

Information
has gloss	eng: The Vaught conjecture is a conjecture in the mathematical field of model theory originally proposed by Robert Lawson Vaught in 1961. It states that the number of countable models of a first-order complete theory in a countable language is finite or ℵ0 or 2ℵ0. Morley showed that number of countable models is finite or ℵ0 or ℵ1 or 2ℵ0, which solves the conjecture except for the case of ℵ1 models when the continuum hypothesis fails. For this remaining case, has announced a counterexample to the Vaught conjecture and the topological Vaught conjecture.
lexicalization	eng: Vaught conjecture
instance of	(noun) a hypothesis that has been formed by speculating or conjecturing (usually with little hard evidence); "speculations about the outcome of the election"; "he dismissed it as mere conjecture" conjecture, speculation