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

Autores

  • Márcia Cerioli
  • Hugo Nobrega
  • Guilherme Silveira
  • Petrucio Viana

DOI:

https://doi.org/10.5540/03.2017.005.01.0239

Palavras-chave:

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

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.

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Publicado

2017-04-14

Edição

v. 5 n. 1 (2017): CNMAC (2016)

Seção

Trabalhos Completos - Matemática Discreta