Journal of Symbolic Logic

Adding linear orders

Saharon Shelah and Pierre Simon

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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.

Article information

Source
J. Symbolic Logic Volume 77, Issue 2 (2012), 717-725.

Dates
First available in Project Euclid: 4 April 2012

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1333566647

Digital Object Identifier
doi:10.2178/jsl/1333566647

Mathematical Reviews number (MathSciNet)
MR2963031

Zentralblatt MATH identifier
1251.03038

Citation

Shelah, Saharon; Simon, Pierre. Adding linear orders. J. Symbolic Logic 77 (2012), no. 2, 717--725. doi:10.2178/jsl/1333566647. https://projecteuclid.org/euclid.jsl/1333566647


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