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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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
DOI: https://doi.org/10.1090/S0002-9947-1984-0742418-9
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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DOI: https://doi.org/10.1090/S0002-9947-1984-0742418-9
Keywords: Universal sentence, finite models, residually finite, finitely presented
Article copyright: © Copyright 1984 American Mathematical Society