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Weak definability in infinitary languages

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah*
Princeton University, Princeton, New Jersey 08540 Hebrew University, Jerusalem, Israel


We shall prove that if a model of cardinality κ can be expanded to a model of a sentence ψ of by adding a suitable predicate in more than κ ways, then, it has a submodel of power μ which can be expanded to a model of ψ in > μ ways provided that λ, κ, μ satisfy suitable conditions.

Research Article
Copyright © Association for Symbolic Logic 1973

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