Sh:692

• Džamonja, M., & Shelah, S. (2004). On \vartriangleleft^*-maximality. Ann. Pure Appl. Logic, 125(1-3), 119–158. arXiv: math/0009087 DOI: 10.1016/j.apal.2003.11.001 MR: 2033421
• 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.
• Version 2020-12-30 (59p) published version (40p)

@article{Sh:692,
 author = {D{\v{z}}amonja, Mirna and Shelah, Saharon},
 title = {{On $\vartriangleleft^*$-maximality}},
 journal = {Ann. Pure Appl. Logic},
 fjournal = {Annals of Pure and Applied Logic},
 volume = {125},
 number = {1-3},
 year = {2004},
 pages = {119--158},
 issn = {0168-0072},
 mrnumber = {2033421},
 mrclass = {03C45 (03C55)},
 doi = {10.1016/j.apal.2003.11.001},
 note = {\href{https://arxiv.org/abs/math/0009087}{arXiv: math/0009087}},
 arxiv_number = {math/0009087}
}