20. Incompleteness of Arithmetic

  1. Zofia Adamowicz1 and
  2. Paweł Zbierski2

Published Online: 30 SEP 2011

DOI: 10.1002/9781118032541.ch20

Logic of Mathematics: A Modern Course of Classical Logic

Logic of Mathematics: A Modern Course of Classical Logic

How to Cite

Adamowicz, Z. and Zbierski, P. (1997) Incompleteness of Arithmetic, in Logic of Mathematics: A Modern Course of Classical Logic, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118032541.ch20

Author Information

  1. 1

    Institute of Mathematics of the Polish Academy of Sciences

  2. 2

    Department of Mathematics, Warsaw University

Publication History

  1. Published Online: 30 SEP 2011
  2. Published Print: 18 MAR 1997

ISBN Information

Print ISBN: 9780471060260

Online ISBN: 9781118032541

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Keywords:

  • incompleteness theorem;
  • Peano arithmetic;
  • Zermelo-fraenkel set theory;
  • finite sequences;
  • prime numbers

Summary

This chapter contains sections titled:

  • Induction on the course-of-values

  • Defining a Language in N

  • Incompleteness Theorems

  • The Diagonal Lemma

  • The Incompleteness Theorem

  • Tarski's Theorem on the Undefinability

  • Incompleteness Theorem