Abstract
Horn [2] obtained a sufficient condition for an elementary class to be closed under direct product. Chang and Morel [1] showed that this is not a necessary condition. We will show that, if consideration is restricted to identity theory, that is, a first-order predicate calculus with equality but no other relation symbols or operation symbols, Horn's condition is necessary and sufficient.A model for identity theory consists of a non-empty domain A, but no relations or operations except equality. If I is an index set, and for each is a model for identity theory, then the direct product of the is a model for identity theory and has domain A, the cartesian product of the Ai.
Publisher
Cambridge University Press (CUP)
Cited by
7 articles.
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