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Transformation Algebras

Published online by Cambridge University Press:  20 November 2018

Leon LeBlanc
Leon LeBlanc*
Affiliation:
Université de Montréal
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The purpose of this paper is to show that most results concerning polyadic algebras can be generalized to transformation algebras. The results of this paper will clearly indicate that a great deal can be done in polyadic algebras without ever mentioning the quantifier structure (for instance, terms and operations can be characterized without the help of the quantifier structure, at least in the case where an equality is present). In § 1, we develop the elementary theory; in § 2, we study the different ways of extending a (locally finite) transformation algebra (of infinite degree) to a polyadic algebra; in § 3, we study equality transformation algebras; finally, in § 4, we show how terms and operations can be defined in equality transformation algebras.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 602 - 613
Copyright
Copyright © Canadian Mathematical Society 1961

References

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