Positive set‐operators of low complexity
Athanossios Tzouvaras · Mathematical logic quarterly · 2003
Abstract 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(∅︁) ≠ ∅︁, 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.