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