Abstract
It is proposed that a more convenient formalization of predicate calculus is as a free Boolean algebra with extrema for the subsets of variable renaming, these extrema functioning as the quantifiers. In support of this proposal, an ab initio development of the calculus is sketched, a comparison with the standard treatment (which in effect construes the quantifiers as certain closure operators) is made and a proof of the Gödel completeness theorem based on this formalization is presented.
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References
Halmos, P.R., Lectures on Boolean Algebras, Van Nostrand, Princeton, 1963.
Hilbert, D., Ackermann, W., Principles of Mathematical Logic, New York, 1950.
Lyndon, R.C., Notes on Logic, Van Nostrand, Princeton, 1966.
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© 1993 Springer Science+Business Media Dordrecht
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Fleischer, I. (1993). A Boolean Formalization of Predicate Calculus. In: Rosenberg, I.G., Sabidussi, G. (eds) Algebras and Orders. NATO ASI Series, vol 389. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0697-1_4
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DOI: https://doi.org/10.1007/978-94-017-0697-1_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4243-9
Online ISBN: 978-94-017-0697-1
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