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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