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On a classification of theories without the independence property
Author(s) -
Verbovskiy Viktor
Publication year - 2013
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201020060
Subject(s) - independence (probability theory) , mathematics , property (philosophy) , bar (unit) , type (biology) , pure mathematics , combinatorics , epistemology , philosophy , physics , statistics , ecology , meteorology , biology
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.