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.
Citation
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
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