Advertisement

Spectra of Formulae with Henkin Quantifiers

  • Joanna Golińska
  • Konrad Zdanowski
Chapter
Part of the Synthese Library book series (SYLI, volume 320)

Abstract

Scholz defined the spectrum of a formula φ as the set of cardinalities of all finite structures in which φ is true and the spectrum of a logic as the set of spectra of all formulae of this logic. The spectrum problem is usually considered as one of the following:
  1. 1

    Scholz problem: to give a characterization of the spectrum of a given logic.

     
  2. 2

    Asser problem: is the spectrum of a given logic closed under complement?

     

Keywords

Equivalence Class Arithmetical Operation Generalize Spectrum Finite Model Universal Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Blass, A. and Gurevitch, Y. (1986). Henkin quantifiers and complete problems. Annals of Pure and Applied Logic, 32: 1–16.CrossRefGoogle Scholar
  2. Fagin, R,. (1974). Generalized first-order spectra and polynomial-time recognizable sets. SIAM-AMS Proceedings, 7: 43–73.Google Scholar
  3. Golinska, J. (1999). The Spectrum Problem for the Languages with Henkin Quantifiers. Master Thesis, University of Warsaw, Warszawa.Google Scholar
  4. Golinska, J. (2000). On some operations on spectra of logics with Henkin quantifiers. Unpublished.Google Scholar
  5. Krynicki, M. and Mostowski, M. (1992). Decidability problems in languages with Henkin quantifiers. Annals of Pure and Applied Logic, 58: 149–172.CrossRefGoogle Scholar
  6. Krynicki, M. and Mostowski, M. (1995). Henkin quantifiers. In Krynicki, M., Mostowski, M., and Szczerba, L. W., editors, Quantifiers 1, pp. 193–262, Kluwer Academic Publishers, Dordrecht.Google Scholar
  7. Mostowski, M. (2000). Difference sets and some arithmetical operations on spectra. Unpublished.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Joanna Golińska
    • 1
  • Konrad Zdanowski
    • 1
  1. 1.Institute of PhilosophyWarsaw UniversityPoland

Personalised recommendations