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ON THE SYNTAX OF LOGIC AND SET THEORY

Published online by Cambridge University Press:  15 September 2010

LUCIUS T. SCHOENBAUM
LUCIUS T. SCHOENBAUM*
Affiliation:
Louisiana State University
*
*DEPARTMENT OF MATHEMATICS, LOUISIANA STATE UNIVERSITY, BATON ROUGE, LA 70803. E-mail: lschoe2@lsu.edu, URL: http://www.math.lsu.edu/∼lschoe2
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Abstract

We introduce an extension of the propositional calculus to include abstracts of predicates and quantifiers, employing a single rule along with a novel comprehension schema and a principle of extensionality, which are substituted for the Bernays postulates for quantifiers and the comprehension schemata of ZF and other set theories. We prove that it is consistent in any finite Boolean subset lattice. We investigate the antinomies of Russell, Cantor, Burali-Forti, and others, and discuss the relationship of the system to other set-theoretic systems ZF, NBG, and NF. We discuss two methods of axiomatizing higher order quantification and abstraction, and then very briefly discuss the application of one of these methods to areas of mathematics outside of logic.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 3 , Issue 4 , December 2010 , pp. 568 - 599
Copyright
Copyright © Association for Symbolic Logic 2010

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