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Article · Mathematical logic quarterly · February 1, 2013

On a classification of theories without the independence property

Viktor Verbovskiy
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Abstract

Abstract A theory is stable up to Δ if any Δ‐type over a model has a few extensions up to complete types. We prove that a theory has no the independence property iff it is stable up to some Δ, where each \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\varphi (x;\bar{y}) \in \Delta$\end{document} has no the independence property.

Advanced Topology and Set TheoryRings, Modules, and AlgebrasLimits and Structures in Graph Theoryindependence propertystable theoriescomplete types

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