Adding linear orders

by Shelah and Simon. [SiSh:979]
J Symbolic Logic, 2012
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 omega-stable NDOP theory for which every expansion by a linear order interprets bounded arithmetic.


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