A THEORY of PAIRS for NON-VALUATIONAL STRUCTURES

Elitzur Bar-Yehuda, Assaf Hasson, Ya'Acov Peterzil

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Given a weakly o-minimal structure and its o-minimal completion , we first associate to a canonical language and then prove that Th determines. We then investigate the theory of the pair in the spirit of the theory of dense pairs of o-minimal structures, and prove, among other results, that it is near model complete, and every definable open subset of is already definable in. We give an example of a weakly o-minimal structure interpreting and show that it is not elementarily equivalent to any reduct of an o-minimal trace.

Original languageEnglish
Pages (from-to)664-683
Number of pages20
JournalJournal of Symbolic Logic
Volume84
Issue number2
DOIs
StatePublished - 1 Jun 2019
Externally publishedYes

Keywords

  • dense pairs
  • non-valuational
  • o-minimal traces
  • weakly o-minimal structures

ASJC Scopus subject areas

  • Philosophy
  • Logic

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