Advertisement

Proofs

  • Ieke Moerdijk
  • Jaap van Oosten
Chapter
Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Abstract

Proof trees are defined, and the system of natural deduction is introduced. Several examples of deductions are given. The completeness theorem (Henkin-style) is proved. Skolem theories and conservative extensions are treated.

References

  1. 14.
    Dawson, J.W.: Logical Dilemmas – The Life and Work of Kurt Gödel. Peters, Wellesley (1997)Google Scholar
  2. 21.
    Gentzen, G.: Untersuchungen über das logische Schließen. Mathematische Zeitschrift 39, 176–210 (1934)MathSciNetCrossRefGoogle Scholar
  3. 22.
    Gödel, K.: Die Vollständigkeit der Axiome des logischen Funktionenkalküls. Monatshefte für Mathematik und Physik 37, 349–360 (1930)MathSciNetCrossRefGoogle Scholar
  4. 32.
    Henkin, L.: The completeness of the first-order functional calculus. J. Symb. Log. 14, 159–166 (1949)MathSciNetCrossRefGoogle Scholar
  5. 54.
    Menzler–Trott, E.: Logic’s Lost Genius: The Life of Gerhard Gentzen. History of Mathematics, vol. 33. American Mathematical Society and London Mathematical Society, Providence (2007)Google Scholar
  6. 83.
    Wang, H.: Reflections on Kurt Gödel. MIT Press, Cambridge (1987)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Ieke Moerdijk
    • 1
  • Jaap van Oosten
    • 1
  1. 1.Department of MathematicsUtrecht UniversityUtrechtThe Netherlands

Personalised recommendations