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Mathematics of Ramsey Theory pp 232–245Cite as

Combinatorial Statements Independent of Arithmetic

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Part of the book series: Algorithms and Combinatorics ((AC,volume 5))

Abstract

When Peano’s first order axioms of arithmetic (P) were originally formulated it was generally felt that these axioms summed up all that was obviously true about the natural numbers (ℕ) with addition and multiplication and that any true first order statement of arithmetic would follow from these axioms. This belief held sway until in 1931 Gödel exhibited a first order statement of arithmetic (or as we shall now call it an arithmetic statement) Θ G which was true but neither it nor its negation could be proved for P. That is Θ G was an arithmetic statement independent of arithmetic.

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Authors
  1. Jeff Paris
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Editors and Affiliations

  1. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 11800, Praha 1, Czechoslovakia

    Jaroslav Nešetřil

  2. Department of Mathematics and Computer Science, Emory University, Atlanta, GA, 30322, USA

    Vojtěch Rödl

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© 1990 Springer-Verlag Berlin Heidelberg

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Paris, J. (1990). Combinatorial Statements Independent of Arithmetic. In: Nešetřil, J., Rödl, V. (eds) Mathematics of Ramsey Theory. Algorithms and Combinatorics, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72905-8_16

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  • DOI: https://doi.org/10.1007/978-3-642-72905-8_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-72907-2

  • Online ISBN: 978-3-642-72905-8

  • eBook Packages: Springer Book Archive

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