On triangleleft^*-maximality

Mirna Džamonja; Saharon Shelah

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On triangleleft^*-maximality

Mirna Džamonja·Saharon Shelah

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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.

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BibTeX RIS

Mirna Džamonja, Saharon Shelah. 2011-04-14. On triangleleft^*-maximality. https://arxiv.org/abs/math/0009087

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