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Transactions of the American Mathematical Society

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On the universal theory of classes of finite models

Author: S. Tulipani
Journal: Trans. Amer. Math. Soc. 284 (1984), 163-170
MSC: Primary 03C13; Secondary 03C05, 03C60
MathSciNet review: 742418
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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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Keywords: Universal sentence, finite models, residually finite, finitely presented
Article copyright: © Copyright 1984 American Mathematical Society