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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Provability with finitely many variables


Author: J. Donald Monk
Journal: Proc. Amer. Math. Soc. 27 (1971), 353-358
MSC: Primary 02.18
DOI: https://doi.org/10.1090/S0002-9939-1971-0276063-5
MathSciNet review: 0276063
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Abstract: In first-order logic with equality but with finitely many variables, no finite schema suffices to give a sound and complete axiomatization of the universally valid sentences. The proof uses a rather deep result from algebraic logic.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0276063-5
Keywords: Provability, first-order logic, polyadic algebras, set polyadic algebras, representable polyadic algebras, logically valid sentences, equations holding in polyadic algebras
Article copyright: © Copyright 1971 American Mathematical Society