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  1. On definability of types and relative stability.Viktor Verbovskiy - 2019 - Mathematical Logic Quarterly 65 (3):332-346.
    In this paper, we consider the question of definability of types in non‐stable theories. In order to do this we introduce a notion of a relatively stable theory: a theory is stable up to Δ if any Δ‐type over a model has few extensions up to complete types. We prove that an n‐type over a model of a theory that is stable up to Δ is definable if and only if its Δ‐part is definable.
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  • Weak definability in infinitary languages.Saharon Shelah - 1973 - Journal of Symbolic Logic 38 (3):399-404.
    We shall prove that if a model of cardinality κ can be expanded to a model of a sentence ψ of Lλ+,ω 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 $> \mu$ ways provided that λ,κ,μ satisfy suitable conditions.
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  • Examples in dependent theories.Itay Kaplan & Saharon Shelah - 2014 - Journal of Symbolic Logic 79 (2):585-619.
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