# Sh:500

- Shelah, S. (1996).
*Toward classifying unstable theories*. Ann. Pure Appl. Logic,**80**(3), 229–255. arXiv: math/9508205 DOI: 10.1016/0168-0072(95)00066-6 MR: 1402297 -
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. - 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} }