Notre Dame Journal of Formal Logic

Semantics for Two Second-Order Logical Systems: $\equiv$RRC* and Cocchiarella's RRC*

Max A. Freund

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.

Article information

Source
Notre Dame J. Formal Logic, Volume 37, Number 3 (1996), 483-505.

Dates
First available in Project Euclid: 14 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1039886523

Digital Object Identifier
doi:10.1305/ndjfl/1039886523

Mathematical Reviews number (MathSciNet)
MR1434432

Zentralblatt MATH identifier
0869.03006

Subjects
Primary: 03B15: Higher-order logic and type theory

Citation

Freund, Max A. Semantics for Two Second-Order Logical Systems: $\equiv$ RRC* and Cocchiarella's RRC*. Notre Dame J. Formal Logic 37 (1996), no. 3, 483--505. doi:10.1305/ndjfl/1039886523. https://projecteuclid.org/euclid.ndjfl/1039886523


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References

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