On triangleleft^*-maximality

Details On triangleleft^*-maximality On triangleleft^*-maximality

2000-09-08

arxiv.org/abs/math/0009087v2

Mathematics

Logic

Scientific paper

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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