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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

1. Halmos, P. R., Algebraic logic I, Monadic Boolean Algebras, Composito Mathematica, 12 (1955), 217–249.Google Scholar
2. Halmos, P. R., Algebraic logic II, Homogeneous locally finite polyadic Boolean algebras of infinite degree, Fund. Math., 43 (1957), 255–325.Google Scholar
3. Halmos, P. R., Algebraic logic III, Predicates, terms, and operations in polyadic algebras, Trans. Amer. Math. Soc, 83 (1956), 430–470.Google Scholar
4. Halmos, P. R., Algebraic logic IV, Equality in polyadic algebras, Trans. Amer. Math. Soc, 86 (1957) 1–27.Google Scholar
5. LeBlanc, L., Dualité pour les égalités Booléennes, Comptes rendus des séances de l'académie des sciences de Paris (May 30, 1960).Google Scholar
6. LeBlanc, L., Les algèbres Booléennes topologiques bornées, Comptes rendus des séances de l'académie des sciences de Paris (June 8, 1960).Google Scholar
7. LeBlanc, L., Les algèbres de transformations, Comptes rendus des séances de l'académie des sciences de Paris (June 13, 1960).Google Scholar
8. LeBlanc, L., Représentation des algèbres polyadiques pour anneau, Comptes rendus des séances de l'académie des sciences de Paris (June 20, 1960).Google Scholar
9. McNeille, H. M., Partially ordered sets, Trans. Amer. Math. Soc, 42 (1937).Google Scholar