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Archive for Mathematical Logic

, Volume 55, Issue 5–6, pp 735–748 | Cite as

Definable choice for a class of weakly o-minimal theories

  • Michael C. Laskowski
  • Christopher S. ShawEmail author
Article

Abstract

Given an o-minimal structure \({\mathcal M}\) with a group operation, we show that for a properly convex subset U, the theory of the expanded structure \({\mathcal M}'=({\mathcal M},U)\) has definable Skolem functions precisely when \({\mathcal M}'\) is valuational. As a corollary, we get an elementary proof that the theory of any such \({\mathcal M}'\) does not satisfy definable choice.

Keywords

Weakly o-minimal Skolem functions Definable choice 

Mathematics Subject Classification

03C64 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA
  2. 2.Department of Science and MathematicsColumbia College ChicagoChicagoUSA

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