On properties of theories which preclude the existence of universal models

Džamonja, Mirna and Shelah, Saharon (2006) On properties of theories which preclude the existence of universal models. Annals of Pure and Applied Logic, 139 (1-3). pp. 280-302.

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We introduce the oak property of first order theories, which is a syntactical condition that we show to be sufficient for a theory not to have universal models in cardinality ? when certain cardinal arithmetic assumptions about ? implying the failure of GCH (and close to the failure of SCH) hold. We give two examples of theories that have the oak property and show that none of these examples satisfy SOP4, not even SOP3. This is related to the question of the connection of the property SOP4 to non-universality, as was raised by the earlier work of Shelah. One of our examples is the theory View the MathML source for which non-universality results similar to the ones we obtain are already known; hence we may view our results as an abstraction of the known results from a concrete theory to a class of theories. We show that no theory with the oak property is simple.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Logic
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 10:19
Last Modified: 15 Dec 2022 17:31
URI: https://ueaeprints.uea.ac.uk/id/eprint/19960
DOI: 10.1016/j.apal.2005.06.001


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