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Equational bases of boolean algebras

Published online by Cambridge University Press:  12 March 2014

F. M. Sioson
F. M. Sioson*
Affiliation:
University of Florida
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Extract

It is well-known that a Boolean algebra (B, +, ., ‐) may be defined as an algebraic system with at least two elements such that (for all x, y, z ε B):

These axioms or equations are not independent, in the sense that some of them are logical consequences of the others. B. A. Bernstein [1] thought that the first three and their duals form an independent dual-symmetric definition of a Boolean algebra, but R. Montague and J. Tarski [3] proved later that B1 (or B̅1) follows from B2, B3, B̅1, B̅2, B̅3 (from B1, B2, B3, B̅2, B̅3).

Type
Articles
Information
The Journal of Symbolic Logic , Volume 29 , Issue 3 , September 1964 , pp. 115 - 124
Copyright
Copyright © Association for Symbolic Logic 1964

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References

[1]Bernstein, B. A., A simplification of the Whitehead- Huntington set of postulates for Boolean algebras, Bulletin of the American Mathematical Society, vol. 22 (1916), pp. 458–459.CrossRefGoogle Scholar
[2]Bernstein, B. A., A dual-symmetric definition of Boolean algebra free from postulated special elements, Scripta mathematica, vol 16 (1950), pp. 157–160.Google Scholar
[3]Montague, R. and Tarski, J., On Bernstein's self-dual set of postulates for Boolean algebras, Proceedings of the American Mathematical Society, vol. 5 (1954), pp. 310–311.Google Scholar