## Notre Dame Journal of Formal Logic

### Rules and Arithmetics

Albert Visser

#### Abstract

This paper is concerned with the logical structure of arithmetical theories. We survey results concerning logics and admissible rules of constructive arithmetical theories. We prove a new theorem: the admissible propositional rules of Heyting Arithmetic are the same as the admissible propositional rules of Intuitionistic Propositional Logic. We provide some further insights concerning predicate logical admissible rules for arithmetical theories

#### Article information

Source
Notre Dame J. Formal Logic, Volume 40, Number 1 (1999), 116-140.

Dates
First available in Project Euclid: 5 December 2002

https://projecteuclid.org/euclid.ndjfl/1039096308

Digital Object Identifier
doi:10.1305/ndjfl/1039096308

Mathematical Reviews number (MathSciNet)
MR1811206

Zentralblatt MATH identifier
0968.03071

Subjects
Primary: 03F50: Metamathematics of constructive systems
Secondary: 03F30: First-order arithmetic and fragments

#### Citation

Visser, Albert. Rules and Arithmetics. Notre Dame J. Formal Logic 40 (1999), no. 1, 116--140. doi:10.1305/ndjfl/1039096308. https://projecteuclid.org/euclid.ndjfl/1039096308

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