On a classification of theories without the independence property

2013

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DOI 10.1002/malq.201020060
Data confidence 70 medium
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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.