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Positive set-operators of low complexity

✍ Scribed by Athanossios Tzouvaras

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 166 KB
Volume: 49
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200310028

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✦ Synopsis

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.

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