The partial clone of linear formulas

  • A term t is linear if no variable occurs more than once in t. An identity s ≈ t is said to be linear if s and t are linear terms. Identities are particular formulas. As for terms superposition operations can be defined for formulas too. We define the arbitrary linear formulas and seek for a condition for the set of all linear formulas to be closed under superposition. This will be used to define the partial superposition operations on the set of linear formulas and a partial many-sorted algebra Formclonelin(τ, τ′). This algebra has similar properties with the partial many-sorted clone of all linear terms. We extend the concept of a hypersubstitution of type τ to the linear hypersubstitutions of type (τ, τ′) for algebraic systems. The extensions of linear hypersubstitutions of type (τ, τ′) send linear formulas to linear formulas, presenting weak endomorphisms of Formclonelin(τ, τ′).

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Author details:Klaus DeneckeORCiDGND
Parent title (English):Siberian mathematical journal
Publisher:Pleiades Publ.
Place of publication:New York
Document type:Article
Date of first publication:2019/08/13
Year of completion:2019
Release date:2021/01/13
Tag:clone; formula; linear formula; linear hypersubstitution; linear term; partial clone; superposition; term
Page number:13
First page:572
Last Page:584
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Peer review:Referiert