A THEORY of PAIRS for NON-VALUATIONAL STRUCTURES

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

doi:10.1017/jsl.2018.85

A THEORY of PAIRS for NON-VALUATIONAL STRUCTURES

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

Ben-Gurion University of the Negev, University of Haifa

Research output: Contribution to journal › Article › peer-review

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 language	American English
Pages (from-to)	664-683
Number of pages	20
Journal	Journal of Symbolic Logic
Volume	84
Issue number	2
DOIs	https://doi.org/10.1017/jsl.2018.85
State	Published - 1 Jun 2019

Keywords

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

All Science Journal Classification (ASJC) codes

Philosophy
Logic

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10.1017/jsl.2018.85

Cite this

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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.",

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A THEORY of PAIRS for NON-VALUATIONAL STRUCTURES

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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