### On quantification with a finite universe

by Shelah. [Sh:639]

J Symbolic Logic, 2000

We consider a finite universe U (more exactly - a
family U of them). Can second order quantifier Q_K, where for
each U this means quantifying over a family of
n(K)-place relations closed under permuting U . We define
some natural orders and shed some light on the classification
problem of those quantifiers.

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