Definability of Polyadic Lifts of Generalized Quantifiers

Authors:
Lauri Hella;Jouko Väänänen;Dag Westerståhl
Affiliations:
Department of Mathematics, P.O. Box 4 (Yliopistonkatu 5), 00014 University of Helsinki, Finland (E-mail: {hella, jvaanane}@cc.helsinki.fi);Department of Mathematics, P.O. Box 4 (Yliopistonkatu 5), 00014 University of Helsinki, Finland (E-mail: {hella, jvaanane}@cc.helsinki.fi);Department of Philosophy, University of Stockholm, S-106 91 Stockholm, Sweden (E-mail: dag.westerstahl@philosophy.su.se)
Venue:
Journal of Logic, Language and Information
Year:
1997

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Abstract

We study generalized quantifiers on finite structures.With every function f : ω → ωwe associate a quantifier Q_f by letting Q_fx&phis; say ’’there are at least f(n) elementsx satisfying &phis;, where n is the sizeof the universe.‘‘ This is the general form ofwhat is known as a monotone quantifier of type 〈 1 〉.We study so called polyadic liftsof such quantifiers. The particular lifts we considerare Ramseyfication, branching and resumption.In each case we get exact criteria fordefinability of the lift in terms of simpler quantifiers.