On uncountable hypersimple unidimensional theories
Logic
2013-11-12 v1
Abstract
We extend a dichotomy between 1-basedness and supersimplicity proved in a previous paper. The generalization we get is to arbitrary language, with no restrictions on the topology (we do not demand type-definabilty of the open set in the definition of essential 1-basedness). We conclude that every (possibly uncountable) hypersimple unidimensional theory that is not s-essentially 1-based by means of the forking topology is supersimple. We also obtain a strong version of the above dichotomy in the case where the language is countable.
Keywords
Cite
@article{arxiv.1311.2225,
title = {On uncountable hypersimple unidimensional theories},
author = {Ziv Shami},
journal= {arXiv preprint arXiv:1311.2225},
year = {2013}
}