Quantifier rank for parity of embedded finite models

Authors:
Hervé Fournier
Affiliations:
Laboratoire de l'Informatique du Parallélisme, Unité de Rech. Associée, École Normale Supérieure de Lyon, 46, allée d'Italie, 69364 Lyon Cedex 07, France
Venue:
Theoretical Computer Science - Mathematical foundations of computer science
Year:
2003

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Abstract

We are interested in the quantifier rank necessary to express the parity of an embedded set of cardinal smaller than a given bound. We consider several embedding structures such as the reals with addition and order, or the field of complex numbers. We provide both lower and upper bounds. We obtain from these results some bounds on the quantifier rank needed to express the connectivity of an embedded graph, when a bound on its number of vertices is given.