Relevant Robinson's arithmetic

Studia Logica 38 (4):407 - 418 (1979)
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Abstract

In this paper two different formulations of Robinson's arithmetic based on relevant logic are examined. The formulation based on the natural numbers (including zero) is shown to collapse into classical Robinson's arithmetic, whereas the one based on the positive integers (excluding zero) is shown not to similarly collapse. Relations of these two formulations to R. K. Meyer's system R# of relevant Peano arithmetic are examined, and some remarks are made about the role of constant functions (e.g., multiplication by zero) in relevant arithmetic.

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Author's Profile

Jon Michael Dunn
PhD: University of Pittsburgh; Last affiliation: Indiana University, Bloomington

Citations of this work

Relevant Robinson's arithmetic.J. Michael Dunn - 1979 - Studia Logica 38 (4):407 - 418.
From Hilbert proofs to consecutions and back.Tore Fjetland Øgaard - 2021 - Australasian Journal of Logic 18 (2):51-72.
Substitution in relevant logics.Tore Fjetland Øgaard - 2019 - Review of Symbolic Logic (3):1-26.
Conditionals, quantification, and strong mathematical induction.Daniel H. Cohen - 1991 - Journal of Philosophical Logic 20 (3):315 - 326.

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References found in this work

Computability and Logic.George Boolos, John Burgess, Richard P. & C. Jeffrey - 1980 - New York: Cambridge University Press. Edited by John P. Burgess & Richard C. Jeffrey.
Foundations of mathematical logic.Haskell Brooks Curry - 1963 - New York: Dover Publications.
Entailment. Vol. 1.Alan Ross Anderson & Nuel D. Belnap - 1977 - Canadian Journal of Philosophy 7 (2):405-411.

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