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.
Bibliographical noteFunding Information:
The first and second authors were supported by ISF grantNo. 181/16.
Copyright © The Association for Symbolic Logic 2019.
- dense pairs
- o-minimal traces
- weakly o-minimal structures
ASJC Scopus subject areas