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\(E\)-closed sets of hyperfunctions on two-element set. (English) Zbl 07334086

Summary: Hyperfunctions are functions that are defined on a finite set and return all non-empty subsets of the considered set as their values. This paper deals with the classification of hyperfunctions on a two-element set. We consider the composition and the closure operator with the equality predicate branching \((E\)-operator). \(E\)-closed sets of hyperfunctions are sets that are obtained using the operations of adding dummy variables, identifying variables, composition, and \(E\)-operator. It is shown that the considered classification leads to a finite set of closed classes. The paper presents all \(78 E\)-closed classes of hyperfunctions, among which there are 28 pairs of dual classes and 22 self-dual classes. The inclusion diagram of the \(E\)-closed classes is constructed, and for each class its generating system is obtained.

MSC:

03Bxx General logic
08Axx Algebraic structures
03Cxx Model theory
03-XX Mathematical logic and foundations
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References:

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