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Journal of Logic and Computation

Volume 13, Issue 2, April 2003: pp. 273-285

On Almost Sure Elimination of Numerical Quantifiers

Risto Kaila1

1Department of Mathematics, University of Helsinki, P.O. Box 4, 00014 University of Helsinki, Finland. E-mail: risto.kaila@helsinki.fi

A criterion is given for a collection Q of simple numerical quantifiers such that the logic L[infin][ohgr][ohgr](Q) has almost sure quantifier elimination and the zero-one law for some sequences of probability measures of finite structures. For instance, the results can be applied to random graphs with a constant, or sufficiently smooth, edge probability.

Keywords: Zero-one laws; quantifier elimination; Lindström quantifiers; infinitary logics

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