Author:
Shelah Saharon,Simon Pierre
Abstract
AbstractWe 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.
Publisher
Cambridge University Press (CUP)
Cited by
4 articles.
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1. Preservation of NATP;Journal of Mathematical Logic;2023-12-20
2. Wild theories with o-minimal open core;Annals of Pure and Applied Logic;2018-02
3. Externally definable sets and dependent pairs II;Transactions of the American Mathematical Society;2015-02-20
4. Distal and non-distal NIP theories;Annals of Pure and Applied Logic;2013-03