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- Arnaud Durand, Ronald Fagin, Bernd Loescher
- CSL
- 1997

The spectrum of a rst-order sentence is the set of cardinalities of its nite models. This paper is concerned with spectra of sentences over languages that contain only unary function symbols. In particular, it is shown that a set S of natural numbers is the spectrum of a sentence over the language of one unary function symbol precisely if S is an eventually… (More)

- Bernd Loescher
- Inf. Process. Lett.
- 1997

We show that the set of square numbers is the spectrum of an F 1 1;1-sentence (existential second order logic with quantiication over unary function variables) with two unary function variables, but it is not the spectrum of F 1 1;1-sentences with only one unary function variable.

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