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Published online by Cambridge University Press: 12 March 2014
We consider a finite universe  (more exactly—a family
 (more exactly—a family  of them), second order quantifiers QK, where for each
 of them), second order quantifiers QK, where for each  this means quantifying over a family of n(K)-place relations closed under permuting
 this means quantifying over a family of n(K)-place relations closed under permuting  . We define some natural orders and shed some light on the classification problem of those quantifiers.
. We define some natural orders and shed some light on the classification problem of those quantifiers.