Adding linear orders
Logic
2012-08-14 v1
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 \omega-stable NDOP theory for which every expansion by a linear order interprets bounded arithmetic.
Keywords
Cite
@article{arxiv.1103.0206,
title = {Adding linear orders},
author = {Saharon Shelah and Pierre Simon},
journal= {arXiv preprint arXiv:1103.0206},
year = {2012}
}