Notre Dame Journal of Formal Logic

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

Edwin D. Mares


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.

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

First available in Project Euclid: 16 May 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Bertrand Russell higher-order logic logicism


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.

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