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Adding linear orders

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah
Affiliation:
Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University Of Jerusalem, Jerusalem, 91904, Israel, E-mail: shelah@math.huji.ac.il, URL: http://shelah.logic.at
Pierre Simon
Affiliation:
Département De Mathématiques et Applications 45, Rue d'Ulm, 75005 Paris, France, E-mail: pierre.simon.05@normalesup.org, URL: http://www.normalesup.org/˜simon/

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.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2012

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References

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