Finite Arithmetic with Infinite Descent

Dialectica 43 (4):329-337 (1989)
Authors
Yvon Gauthier
Université de Montréal
Abstract
SummaryFinite, or Fermat arithmetic, as we call it, differs from Peano arithmetic in that it does not involve the existence of an infinite set or Peano's induction postulate. Fermat's method of infinite descent takes the place of bound induction, and we show that a con‐structivist interpretation of logical connectives and quantifiers can account for the predicative finitary nature of Fermat's arithmetic. A non‐set‐theoretic arithemetical logic thus seems best suited to a constructivist‐inspired number theory
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DOI 10.1111/j.1746-8361.1989.tb00949.x
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References found in this work BETA

Mathematical Logic.Joseph R. Shoenfield - 1967 - Reading, Mass., Addison-Wesley Pub. Co..
Proof Theory.Gaisi Takeuti - 1987 - Elsevier.
Predicative Arithmetic.Edward Nelson - 1986 - Princeton University Press.
Selected Works in Logic.Thoralf Skolem - 1970 - Oslo, Universitetsforlaget.
Constructive Formalism.R. L. Goodstein - 1951 - Leicester [Eng.]University College.

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