# Spectra of Formulae with Henkin Quantifiers

Chapter

## 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?

## Keywords

Equivalence Class Arithmetical Operation Generalize Spectrum Finite Model Universal Variable
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## References

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*Annals of Pure and Applied Logic*,**32**: 1–16.CrossRefGoogle Scholar - Fagin, R,. (1974). Generalized first-order spectra and polynomial-time recognizable sets.
*SIAM-AMS Proceedings*,**7**: 43–73.Google Scholar - Golinska, J. (1999).
*The Spectrum Problem for the Languages with Henkin Quantifiers*. Master Thesis, University of Warsaw, Warszawa.Google Scholar - Golinska, J. (2000). On some operations on spectra of logics with Henkin quantifiers. Unpublished.Google Scholar
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*Annals of Pure and Applied Logic*,**58**: 149–172.CrossRefGoogle Scholar - 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 - Mostowski, M. (2000). Difference sets and some arithmetical operations on spectra. Unpublished.Google Scholar

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