The powerset operator, P is compared with other operators of similar type and logical complexity. Namely we examine positive operators whose defining formula has a canonical form containing at most a string of universal quantifiers. We call them -operators. The question we address in this paper is: How is the class of -operators generated? It is shown that every positive -operator Γ such that Γ(φ) ≠ φ, is finitely generated from P, the identity operator Id, constant operators and certain trivial ones by composition, ∪ and ∩. This extends results of [3] concerning bounded positive operators.
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