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Article · Mathematical logic quarterly · September 30, 2019

On definability of types and relative stability

Viktor Verbovskiy
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Abstract

Abstract 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.

Advanced Topology and Set TheoryRings, Modules, and AlgebrasMathematical and Theoretical Analysisrelative stabilitystable theoriescomplete types

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