Premium
Positive set‐operators of low complexity
Author(s) -
Tzouvaras Athanossios
Publication year - 2003
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200310028
Subject(s) - mathematics , operator (biology) , set (abstract data type) , operator norm , bounded function , quasinormal operator , class (philosophy) , operator theory , identity (music) , discrete mathematics , algebra over a field , string (physics) , pure mathematics , finite rank operator , computer science , mathematical analysis , banach space , biochemistry , chemistry , transcription factor , acoustics , mathematical physics , gene , programming language , physics , repressor , artificial intelligence
Abstract The powerset operator, , 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 , the identity operator Id, constant operators and certain trivial ones by composition, ∪ and ∩. This extends results of [3] concerning bounded positive operators.