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June 2012 Adding linear orders
Saharon Shelah, Pierre Simon
J. Symbolic Logic 77(2): 717-725 (June 2012). DOI: 10.2178/jsl/1333566647

Abstract

We address the following question: Can we expand an NIP theory by adding a linear order such that the expansion is still NIP? Easily, if acl(A)=A for all A, then this is true. Otherwise, we give counterexamples. More precisely, there is a totally categorical theory for which every expansion by a linear order has IP. There is also an ω-stable NDOP theory for which every expansion by a linear order interprets pseudofinite arithmetic.

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Saharon Shelah. Pierre Simon. "Adding linear orders." J. Symbolic Logic 77 (2) 717 - 725, June 2012. https://doi.org/10.2178/jsl/1333566647

Information

Published: June 2012
First available in Project Euclid: 4 April 2012

zbMATH: 1251.03038
MathSciNet: MR2963031
Digital Object Identifier: 10.2178/jsl/1333566647

Rights: Copyright © 2012 Association for Symbolic Logic

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Vol.77 • No. 2 • June 2012
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