Logics L_{κ,λ} allowing conjunctions/disjunctions over sets of cardinality <κ and quantification over sequences of length <λ. Loses compactness but gains expressive power (Scott's isomorphism theorem).
Logics L_{κ,λ} allowing conjunctions/disjunctions over sets of cardinality <κ and quantification over sequences of length <λ. Loses compactness but gains expressive power (Scott's isomorphism theorem).