On $\vartriangleleft^\ast$-maximality

by Dzamonja and Shelah. [DjSh:692]
Annals Pure and Applied Logic, 2004
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.

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