Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Syntax of First-Order Logic Read chapter Read first chapter

2013 | OriginalPaper | Chapter

4. Completeness Theorem for First-Order Logic

Author : Shashi Mohan Srivastava

Published in: A Course on Mathematical Logic

Publisher: Springer New York

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In Chap. 1, we described what a first-order language is and what its terms and formulas are. We fixed a first-order language L. In Chap. 2, we described the semantics of first-order languages. In Chap. 3, we considered a simpler form of logic – propositional logic, defined what a proof is in that logic, and proved its completeness theorem. In this chapter we shall define proof in a first-order theory and prove the corresponding completeness theorem. The result for countable theories was first proved by Gödel in 1930. The result in its complete generality was first observed by Malcev in 1936. The proof given below is due to Leo Henkin.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Propositional Logic
next chapter Model Theory
Literature
1.
2.
Bochnak, J., Coste, M., Roy, M-F.: Real Algebraic Geometry, vol. 36, A Series of Modern Surveys in Mathematics. Springer, New York (1998)MATH
3.
Chang, C.C., Keisler, H.J.: Model Theory, 3rd edn. North-Holland, London (1990)MATH
4.
Flath, D., Wagon, S.: How to pick out integers in the rationals: An application of number theory to logic. Am. Math. Mon. 98, 812–823 (1991)MathSciNetMATHCrossRef
5.
Hinman, P.: Fundamentals of Mathematical Logic. A. K. Peters (2005)MATH
6.
Hofstadter, D.R.: Gödel, Escher, Bach: An Eternal Golden Braid. Vintage Books, New York (1989)
7.
8.
Jech, T.: Set Theory, Springer Monographs in Mathematics, 3rd edn. Springer, New York (2002)
9.
Kunen, K.: Set Theory: An Introduction to Independence Proofs. North-Holland, Amsterdam (1980)MATH
10.
Lang, S.: Algebra, 3rd edn. Addison-Wesley (1999)
11.
Marker, D.: Model Theory: An Introduction, GTM 217. Springer, New York (2002)
12.
Rogers, H.J.: Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York (1967)MATH
13.
Penrose, R.: The Emperor’s New Mind. Oxford University Press, Oxford (1990)
14.
Pila, J.: O-minimality and André-Oort conjecture for ℂ n . Ann. Math. (2) 172(3), 1779–1840 (2011)
15.
Pila, J., Zannier, U.: Rational points in periodic analytic sets and the Manin-Mumford conjecture, Atti. Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei(9). Mat. Appl. 19(2), 149–162 (2008)
16.
17.
Srivastava, S.M.: A Course on Borel Sets, GTM 180. Springer, New York (1998)CrossRef
18.
Swan, R.G.: Tarski’s principle and the elimination of quantifiers (preprint)
Metadata
Title
Completeness Theorem for First-Order Logic
Author
Shashi Mohan Srivastava
Copyright Year
2013
Publisher
Springer New York
Book
A Course on Mathematical Logic

Print ISBN: 978-1-4614-5745-9

Electronic ISBN: 978-1-4614-5746-6

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-1-4614-5746-6_4

Premium Partner

    Image Credits