Notre Dame Journal of Formal Logic

Reflexive Intermediate First-Order Logics

Nathan C. Carter


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

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

First available in Project Euclid: 6 January 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: F03F50
Secondary: 03F55: Intuitionistic mathematics

intermediate logics completeness reflexivity


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.

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