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Peano and the Foundations of Arithmetic

In: Giuseppe Peano between Mathematics and Logic

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  • Gabriele Lolli

    (Scuola Normale Superiore of Pisa)

Abstract

At the end of the 1880s two episodes occurred in rapid succession which formed the bases of what we call the foundations of arithmetic: the publication in 1888 of Was sind und was sollen die Zahlen by Richard Dedekind and in 1889 of Arithmetices Principia, nova methodo exposita by Giuseppe Peano. This work was to give Peano lasting fame, in that he had for the first time expounded the axioms for the system of natural numbers; from that time on they were linked to his name, and from the English “Peano Arithmetic” were known by the acronym PA.

Suggested Citation

  • Gabriele Lolli, 2011. "Peano and the Foundations of Arithmetic," Springer Books, in: Fulvia Skof (ed.), Giuseppe Peano between Mathematics and Logic, chapter 4, pages 47-67, Springer.
    • Handle: RePEc:spr:sprchp:978-88-470-1836-5_4
    DOI: 10.1007/978-88-470-1836-5_4
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