Notre Dame Journal of Formal Logic

The Fact Semantics for Ramified Type Theory and the Axiom of Reducibility

Edwin D. Mares

Abstract

This paper uses an atomistic ontology of universals, individuals, and facts to provide a semantics for ramified type theory. It is shown that with some natural constraints on the sort of universals and facts admitted into a model, the axiom of reducibility is made valid.

Article information

Source
Notre Dame J. Formal Logic Volume 48, Number 2 (2007), 237-251.

Dates
First available in Project Euclid: 16 May 2007

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1179323266

Digital Object Identifier
doi:10.1305/ndjfl/1179323266

Mathematical Reviews number (MathSciNet)
MR2306395

Zentralblatt MATH identifier
1137.03004

Subjects
Primary: 03B15: Higher-order logic and type theory 03C85: Second- and higher-order model theory

Keywords
Bertrand Russell higher-order logic logicism

Citation

Mares, Edwin D. The Fact Semantics for Ramified Type Theory and the Axiom of Reducibility. Notre Dame J. Formal Logic 48 (2007), no. 2, 237--251. doi:10.1305/ndjfl/1179323266. http://projecteuclid.org/euclid.ndjfl/1179323266.


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References

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