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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
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51:, 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
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228:{\displaystyle (\omega _{3},\omega _{2})\twoheadrightarrow (\omega _{2},\omega _{1})}
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115:{\displaystyle (\omega _{2},\omega _{1})\twoheadrightarrow (\omega _{1},\omega )}
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proved the consistency of Chang's conjecture from the consistency of an ω
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261:, Studies in Logic and the Foundations of Mathematics (3rd ed.),
47:) for a countable language has an elementary submodel of type (ω
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129:implies that Chang's conjecture fails.
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349:. You can help Knowledge (XXG) by
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284:"Models of complete theories"
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345:-related article is a
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149:-Erdős in
312:0002-9904
214:ω
201:ω
194:↠
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282:(1963),
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257:(1990),
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