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
Scholz problem: to give a characterization of the spectrum of a given logic.
-
2
Asser problem: is the spectrum of a given logic closed under complement?
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Blass, A. and Gurevitch, Y. (1986). Henkin quantifiers and complete problems. Annals of Pure and Applied Logic, 32: 1–16.
Fagin, R,. (1974). Generalized first-order spectra and polynomial-time recognizable sets. SIAM-AMS Proceedings, 7: 43–73.
Golinska, J. (1999). The Spectrum Problem for the Languages with Henkin Quantifiers. Master Thesis, University of Warsaw, Warszawa.
Golinska, J. (2000). On some operations on spectra of logics with Henkin quantifiers. Unpublished.
Krynicki, M. and Mostowski, M. (1992). Decidability problems in languages with Henkin quantifiers. Annals of Pure and Applied Logic, 58: 149–172.
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.
Mostowski, M. (2000). Difference sets and some arithmetical operations on spectra. Unpublished.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Golińska, J., Zdanowski, K. (2003). Spectra of Formulae with Henkin Quantifiers. In: Rojszczak, A., Cachro, J., Kurczewski, G. (eds) Philosophical Dimensions of Logic and Science. Synthese Library, vol 320. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2612-2_3
Download citation
DOI: https://doi.org/10.1007/978-94-017-2612-2_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6432-5
Online ISBN: 978-94-017-2612-2
eBook Packages: Springer Book Archive