Adding linear orders

Saharon Shelah*, Pierre Simon

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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 pseudofinite arithmetic.

Original languageEnglish
Pages (from-to)717-725
Number of pages9
JournalJournal of Symbolic Logic
Volume77
Issue number2
DOIs
StatePublished - Jun 2012

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