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2017•Proceeding Series of the Brazilian Society of Computational and Applied MathematicsOpen access

On the (in)dependence of the Dedekind-Peano axioms for natural numbers

Márcia R. Cerioli, Hugo Nobrega, Guilherme Silveira, Petrúcio Viana

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Abstract

We present a direct proof that the Dedekind-Peano axioms for the sequence of natural numbers are not completely independent, as well as a new completely independent set of axioms based on the same set of primitives as the one originally proposed by R. Dedekind.

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What this paper is about

We present a direct proof that the Dedekind-Peano axioms for the sequence of natural numbers are not completely independent, as well as a new completely independent set of axioms based on the same set of primitives as the one originally proposed by R. Dedekind.

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Available abstract

We present a direct proof that the Dedekind-Peano axioms for the sequence of natural numbers are not completely independent, as well as a new completely independent set of axioms based on the same set of primitives as the one originally proposed by R. Dedekind.

Key concepts: Peano axioms, Dedekind cut, Axiom, Natural number, Axiom of choice, Mathematics, Set (abstract data type), Set theory

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