Notre Dame Journal of Formal Logic

Reflexive Intermediate First-Order Logics

Nathan C. Carter

Abstract

It is known that the set of intermediate propositional logics that can prove their own completeness theorems is exactly those which prove every instance of the principle of testability, ¬ϕ ∨ ¬¬ϕ. Such logics are called reflexive. This paper classifies reflexive intermediate logics in the first-order case: a first-order logic is reflexive if and only if it proves every instance of the principle of double negation shift and the metatheory created from it proves every instance of the principle of testability.

Article information

Source
Notre Dame J. Formal Logic, Volume 49, Number 1 (2008), 75-95.

Dates
First available in Project Euclid: 6 January 2008

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1199649902

Digital Object Identifier
doi:10.1215/00294527-2007-005

Mathematical Reviews number (MathSciNet)
MR2376852

Zentralblatt MATH identifier
1191.03021

Subjects
Primary: F03F50
Secondary: 03F55: Intuitionistic mathematics

Keywords
intermediate logics completeness reflexivity

Citation

Carter, Nathan C. Reflexive Intermediate First-Order Logics. Notre Dame J. Formal Logic 49 (2008), no. 1, 75--95. doi:10.1215/00294527-2007-005. https://projecteuclid.org/euclid.ndjfl/1199649902


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References

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