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December 2010 The characteristic sequence of a first-order formula
M. E. Malliaris
J. Symbolic Logic 75(4): 1415-1440 (December 2010). DOI: 10.2178/jsl/1286198155

Abstract

For a first-order formula φ(x;y) we introduce and study the characteristic sequence 〈 Pn: n < ω 〉 of hypergraphs defined by Pn(y1,…,yn) := (∃ x) ⋁i ≤ n φ(x;yi). We show that combinatorial and classification theoretic properties of the characteristic sequence reflect classification theoretic properties of φ and vice versa. The main results are a characterization of NIP and of simplicity in terms of persistence of configurations in the characteristic sequence. Specifically, we show that some tree properties are detected by the presence of certain combinatorial configurations in the characteristic sequence while other properties such as instability and the independence property manifest themselves in the persistence of complicated configurations under localization.

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M. E. Malliaris. "The characteristic sequence of a first-order formula." J. Symbolic Logic 75 (4) 1415 - 1440, December 2010. https://doi.org/10.2178/jsl/1286198155

Information

Published: December 2010
First available in Project Euclid: 4 October 2010

zbMATH: 1220.03019
MathSciNet: MR2767977
Digital Object Identifier: 10.2178/jsl/1286198155

Rights: Copyright © 2010 Association for Symbolic Logic

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Vol.75 • No. 4 • December 2010
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