On the universal theory of classes of finite models

Tulipani, S.

doi:10.1090/S0002-9947-1984-0742418-9

On the universal theory of classes of finite models
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Trans. Amer. Math. Soc. 284 (1984), 163-170 Request permission

Abstract:

First order theories for which the truth of a universal sentence on their finite models implies the truth on all models are investigated. It is proved that an equational theory has such a property if and only if every finitely presented model is residually finite. The most common classes of algebraic structures are discussed.

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