Original Articles

ULTRA-UNIVERSAL MODELS

Published in: Quaestiones Mathematicae
Volume 15 , issue 2 , 1992 , pages: 189–195

DOI: 10.1080/16073606.1992.9631683

Author(s): Colin Naturman Department of Mathematics, RSA , Henry Rose Department of Mathematics, RSA

Keywords: 03C50 , 03C52

Abstract

The concept of ultra-universal algebras in varieties is generalized to models of first order theories. Characterizations of theories which have ulta-universal models are found and general examples of ultra-universal models are investigated. In particular we show that a theory has an ultra-universal model iff it is consistent and its class of models satisfies the joint embedding property.

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