Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduce the oak property of first order theories, which is a syntactical condition that  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.  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  obtain are already known; hence  may view our results as an abstraction of the known results from a concrete theory to a class of theories.  show that no theory with the oak property is simple.
['Mirna Džamonja', 'Saharon Shelah']
I am writing a research paper on a idea On properties of theories which preclude the existence of universal models
[{"from": "human", "value": "I am writing a research paper on a idea On properties of theories which preclude the existence of universal models"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduce the oak property of first order theories, which is a syntactical condition that  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.  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  obtain are already known; hence  may view our results as an abstraction of the known results from a concrete theory to a class of theories.  show that no theory with the oak property is simple."}]