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 like the reals with addition and order, or the field of the 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.
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Fournier, H. (2001). Quantifier Rank for Parity of Embedded Finite Models. In: Sgall, J., Pultr, A., Kolman, P. (eds) Mathematical Foundations of Computer Science 2001. MFCS 2001. Lecture Notes in Computer Science, vol 2136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44683-4_33
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DOI: https://doi.org/10.1007/3-540-44683-4_33
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