On triangleleft^*-maximality
Logic
2011-04-18 v2
Abstract
This paper investigates a connection between the ordering triangleleft^ast among theories in model theory and the (N)SOP_n hierarchy of Shelah. It introduces two properties which are natural extensions of this hierarchy, called SOP_2 and SOP_1, and gives a strong connection between SOP_1 and the maximality in Keisler ordering. Together with the known results about the connection between the (N)SOP_n hierarchy and the existence of universal models in the absence of GCH, the paper provides a step toward the classification of unstable theories without the strict order property.
Cite
@article{arxiv.math/0009087,
title = {On triangleleft^*-maximality},
author = {Mirna Džamonja and Saharon Shelah},
journal= {arXiv preprint arXiv:math/0009087},
year = {2011}
}