Set Theory pp 29-46 | Cite as

The Dedekind–Peano Axioms

  • Abhijit Dasgupta


This chapter develops the theory of natural numbers based on Dedekind–Peano Axioms, also known as Peano Arithmetic Peano Arithmetic. The basic theory of ratios (positive rational numbers) is also developed. It concludes with a section on formal definition by primitive recursion.


Natural Number Successor Function Recursion Equation Peano Arithmetic Equivalent Fraction 
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    R. Dedekind. The nature and meaning of numbers (1888). In Essays on the Theory of Numbers [12]. English translation of “Was sind und was sollen die Zahlen?”, Vieweg, 1888.Google Scholar
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    E. Landau. Foundations of Analysis. Chelsea Publishing Company, 1966.Google Scholar
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    G. Peano. The principles of arithmetic, presented by a new method (1889). In From Frege to Gödel [78], pages 83–97. English translation of “Arithmetices principia, nova methodo exposita”, Turin, 1889.Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Detroit MercyDetroitUSA

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