English

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}
}