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Summer 1996 Semantics for Two Second-Order Logical Systems: $\equiv$RRC* and Cocchiarella's RRC*
Max A. Freund
Notre Dame J. Formal Logic 37(3): 483-505 (Summer 1996). DOI: 10.1305/ndjfl/1039886523

Abstract

We develop a set-theoretic semantics for Cocchiarella's second-order logical system ${\bf RRC^\ast}$. Such a semantics is a modification of the nonstandard sort of second-order semantics described, firstly, by Simms and later extended by Cocchiarella. We formulate a new second order logical system and prove its relative consistency. We call such a system ${\bf \equiv RRC^\ast}$ and construct its set-theoretic semantics. Finally, we prove completeness theorems for proper normal extensions of the two systems with respect to certain notions of validity provided by the semantics.

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Max A. Freund. "Semantics for Two Second-Order Logical Systems: $\equiv$RRC* and Cocchiarella's RRC*." Notre Dame J. Formal Logic 37 (3) 483 - 505, Summer 1996. https://doi.org/10.1305/ndjfl/1039886523

Information

Published: Summer 1996
First available in Project Euclid: 14 December 2002

zbMATH: 0869.03006
MathSciNet: MR1434432
Digital Object Identifier: 10.1305/ndjfl/1039886523

Subjects:
Primary: 03B15

Rights: Copyright © 1996 University of Notre Dame

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Vol.37 • No. 3 • Summer 1996
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