Skip to main content
SpringerLink
Log in

Elimination problems in logic: a brief history

  • Published:
Synthese Aims and scope Submit manuscript

Abstract

A common aim of elimination problems for languages of logic is to express the entire content of a set of formulas of the language, or a certain part of it, in a way that is more elementary or more informative. We want to bring out that as the languages for logic grew in expressive power and, at the same time, our knowledge of their expressive limitations also grew, elimination problems in logic underwent some change. For languages other than that for monadic second-order logic, there remain important open problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Ackermann W. (1935) Untersuchungen über das Eliminationsproblem der mathematischen Logik. Mathematische Annalen 110: 390–413

    Article  Google Scholar 

  • Behmann H. (1922) Beiträge zur Algebra der Logik. Mathematische Annalen 86: 163–229

    Article  Google Scholar 

  • Boole, G. (1854). An investigation of the laws of thought. London: Walton (Also Open Court, 1916).

  • Burris, S. (Draft 2001). Contributions of the Logicians, Part I: From Richard Whately to William Stanley Jevons.

  • Church, A. (1956). Introduction to mathematical logic. Princeton.

  • Couturat, L. (1914). The algebra of logic. Open Court: Chicago and London.

  • Craig W. (1960) Bases for first-order theories and subtheories. Journal of Symbolic Logic 25: 97–142

    Article  Google Scholar 

  • Henkin L. (1950) Completeness in the theory of types. Journal of Symbolic Logic 15: 81–91

    Article  Google Scholar 

  • Hilbert, D and Bernays, P. (1968). Grundlagen der Mathematik (Vol. 1). Springer-Verlag, Berlin, XV+473pp.

  • Löwenheim, L. (1915). Über Möglichkeiten im Relativkalkül. Mathematische Annalen, 79, 447–470 (English translation, In J. van Heijenort (Ed.), From Frege to Gödel (pp. 228–251)).

  • Müller, E. (1910). Abriss der Algebra der Logik. Leipzig: Teubner (Also in Schröder, E., Algebra der Logik (Vol.III). Chelsea).

  • Schröder, E. (1890, 1891). Vorlesungen über die Algebra der Logik (Vols. I, II). Leipzig: Teubner (Also in NY: Chelsea).

  • Skolem, Th. (1919). Untersuchungenn über die Axiome des Klassenkalküls (Also In J. E. Fenstad (Ed.), Selected works in logic by Th. Skolem, pp. 67–101).

  • Zach, R. (2007). The decision problem and the development of metalogic. ASL Annual Meeting, March 2007.

Download references

Author information

Authors and Affiliations

  1. Department of Philosophy, University of California, 314 Moses Hall, Berkeley, CA, 94720-2930, USA

    William Craig

Authors
  1. William Craig
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to William Craig.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Craig, W. Elimination problems in logic: a brief history. Synthese 164, 321–332 (2008). https://doi.org/10.1007/s11229-008-9352-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11229-008-9352-4

Keywords

Search

Navigation