Completeness theorems for universal and implicational logics of algebras via congruences
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- by Robert W. Quackenbush PDF
- Proc. Amer. Math. Soc. 103 (1988), 1015-1021 Request permission
Abstract:
In this paper, simple algebraic proofs are given for the completeness theorems for the implicational and universal logics of algebras. The proofs are obtained by examining congruences, $\theta$, on the algebra of terms, $F(\omega )$, such that $F(\omega )/\theta$ belongs to the given class of algebras. Thus, they are direct analogs of G. Birkhoff’s proof of the completeness theorem for equational logic.References
- George Grätzer, Universal algebra, 2nd ed., Springer-Verlag, New York-Heidelberg, 1979. MR 538623
- David Kelly, Complete rules of inference for universal sentences, Studia Sci. Math. Hungar. 19 (1984), no. 2-4, 347–361. MR 874503
- A. Selman, Completeness of calculi for axiomatically defined classes of algebras, Algebra Universalis 2 (1972), 20–32. MR 313170, DOI 10.1007/BF02945004
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 1015-1021
- MSC: Primary 03C05; Secondary 08C10, 08C15
- DOI: https://doi.org/10.1090/S0002-9939-1988-0954975-7
- MathSciNet review: 954975