Positive set‐operators of low complexity | Zendy

Tzouvaras Athanossios | Zendy

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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

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.

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