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An axiomatic system for the first order language with an equi-cardinality quantifier

Published online by Cambridge University Press:  12 March 2014

Mitsuru Yasuhara*
Affiliation:
Université de montréal, New York University, University Heights

Extract

The equi-cardinality quantifier1 to be used in this article, written as Qx, is characterised by the following semantical rule: A formula QxA(x) is true in a relational system exactly when the cardinality of the set consisting of these elements which make A(x) true is the same as that of the universe. For instance, QxN(x) is true in 〈Rt, N〉 but false in 〈Rl, N〉 where Rt, Rl, and N are the sets of rational numbers, real numbers, and natural numbers, respectively. We notice that in finite domains the equi-cardinality quantifier is the same as the universal quantifier. For this reason, all relational systems considered in the following are assumed infinite.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1997

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