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Spring 1995 Levels of Truth
Andrea Cantini
Notre Dame J. Formal Logic 36(2): 185-213 (Spring 1995). DOI: 10.1305/ndjfl/1040248454

Abstract

This paper is concerned with the interaction between formal semantics and the foundations of mathematics. We introduce a formal theory of truth, TLR, which extends the classical first order theory of pure combinators with a primitive truth predicate and a family of truth approximations, indexed by a directed partial ordering. TLR naturally works as a theory of partial classifications, in which type-free comprehension coexists with functional abstraction. TLR provides an inner model for a well known subsystem $\mbox{ATR}_0$ of second order arithmetic; indeed, TLR is proof-theoretically equivalent to Predicative Analysis.

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Andrea Cantini. "Levels of Truth." Notre Dame J. Formal Logic 36 (2) 185 - 213, Spring 1995. https://doi.org/10.1305/ndjfl/1040248454

Information

Published: Spring 1995
First available in Project Euclid: 18 December 2002

zbMATH: 0836.03033
MathSciNet: MR1345744
Digital Object Identifier: 10.1305/ndjfl/1040248454

Subjects:
Primary: 03F35
Secondary: 03B40

Rights: Copyright © 1995 University of Notre Dame

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Vol.36 • No. 2 • Spring 1995
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