On one side one can define second-order variables as ranging over all elements of P(adsbygoogle = window.adsbygoogle || []).push({}); ^{k}(M) for all natural numbers k (P=power set of M, M is the universe of the model, superscript being iteration). On the other side it is sometimes defined as ranging over all first-order relations and predicates. In this latter definition, does "predicates" include first-order sentences with quantifiers and variables, or only first-order sentences with only constant symbols?

Thanks.

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# Second-order variables: elements of domain only without quantifiers?

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