On properties of theories which preclude the existence of universal models

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 1 

• Type: Journal
• Year: 2006
• Where: APAL
• Authors: Mirna Dzamonja, Saharon Shelah
• Keywords: APAL 2006, Cardinal Arithmetic Assumptions, Oak Property, Order Theories