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Chang's conjecture

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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 (ω2,ω1) for a countable language has an elementary submodel of type (ω1,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 ( ω 2 , ω 1 ) ↠ ( ω 1 , ω ) {\displaystyle (\omega _{2},\omega _{1})\twoheadrightarrow (\omega _{1},\omega )} .