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

Márcia Cerioli, Hugo Nobrega, Guilherme Silveira, Petrucio Viana

Resumo


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.


Palavras-chave


Peano Axioms, Weak independence, Strong independence, Syntactical proofs.

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DOI: https://doi.org/10.5540/03.2017.005.01.0239

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