Premium
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.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom