# Sh:500

• Shelah, S. (1996). Toward classifying unstable theories. Ann. Pure Appl. Logic, 80(3), 229–255.
• Abstract:
The paper deals with two issues: the existence of universal models of a theory T and related properties when cardinal arithmetic does not give this existence offhand. In the first section we prove that simple theories (e.g., theories without the tree property, a class properly containing the stable theories) behaves “better” than theories with the strict order property, by criterion from [Sh:457]. In the second section we introduce properties SOP_n such that the strict order property implies SOP_{n+1}, which implies SOP_n, which in turn implies the tree property. Now SOP_4 already implies non-existence of universal models in cases where earlier the strict order property was needed, and SOP_3 implies maximality in the Keisler order, again improving an earlier result which had used the strict order property.
• Version 1996-06-22_10 (30p) published version (27p)
Bib entry
@article{Sh:500,
author = {Shelah, Saharon},
title = {{Toward classifying unstable theories}},
journal = {Ann. Pure Appl. Logic},
fjournal = {Annals of Pure and Applied Logic},
volume = {80},
number = {3},
year = {1996},
pages = {229--255},
issn = {0168-0072},
mrnumber = {1402297},
mrclass = {03C45 (03E35)},
doi = {10.1016/0168-0072(95)00066-6},
note = {\href{https://arxiv.org/abs/math/9508205}{arXiv: math/9508205}},
arxiv_number = {math/9508205}
}