In model theory, a branch of mathematical logic, Chang's conjecture, attributed to Chen Chung Chang by Vaught (1963, p. 309), states that every model of type (ω_{2},ω_{1}) for a countable language has an elementary submodel of type (ω_{1}, ω). A model is of type (α,β) if it is of cardinality α and a unary relation is represented by a subset of cardinality β. The usual notation is .
The axiom of constructibility implies that Chang's conjecture fails. Silver proved the consistency of Chang's conjecture from the consistency of an ω_{1}Erdős cardinal. HansDieter Donder showed the reverse implication: if CC holds, then ω_{2} is ω_{1}Erdõs in K.
More generally, Chang's conjecture for two pairs (α,β), (γ,δ) of cardinals is the claim that every model of type (α,β) for a countable language has an elementary submodel of type (γ,δ). The consistency of was shown by Laver from the consistency of a huge cardinal.
