Journal of Symbolic Logic

Adding linear orders

Saharon Shelah and Pierre Simon

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

First available in Project Euclid: 4 April 2012

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

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