On properties of theories which preclude the existence of universal models [article]

Mirna Džamonja, Saharon Shelah
2000 arXiv   pre-print
In this paper we investigate some properties of first order theories which prevent them from having universal models under certain cardinal arithmetic assumptions. Our results give a new syntactical condition, oak property, which is a sufficient condition for a theory not to have universal models in cardinality lambda when certain cardinal arithmetic assumptions implying the failure of GCH (and close to the failure of SCH) hold.
arXiv:math/0009078v1 fatcat:ec5ejymzozdmdo3q37o4uj6rp4