Maximal small extensions of o-minimal structures
Logic
2011-04-22 v3
Abstract
A proper elementary extension of a model is called small if it realizes no new types over any finite set in the base model. We answer a question of Marker, and show that it is possible to have an o-minimal structure with a maximal small extension. Our construction yields such a structure for any cardinality. We show that in some cases, notably when the base structure is countable, the maximal small extension has maximal possible cardinality.
Cite
@article{arxiv.0712.0591,
title = {Maximal small extensions of o-minimal structures},
author = {Janak Ramakrishnan},
journal= {arXiv preprint arXiv:0712.0591},
year = {2011}
}
Comments
6 pages. To appear in Mathematical Logic Quarterly