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arXiv · 1103.0206

Adding linear orders

Saharon Shelah·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 bounded arithmetic.

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Saharon Shelah, Pierre Simon. 2011-03-01. Adding linear orders. https://arxiv.org/abs/1103.0206

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