2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59890In 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.Logictext