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Universal Functions and Σω-Bounded Structures

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Algebra and Logic Aims and scope

We introduce the notion of a Σω-bounded structure and specify a necessary and sufficient condition for a universal Σ-function to exist in a hereditarily finite superstructure over such a structure, for the class of all unary partial Σ-functions assuming values in the set ω of natural ordinals. Trees and equivalences are exemplified in hereditarily finite superstructures over which there exists no universal Σ-function for the class of all unary partial Σ-functions, but there exists a universal Σ-function for the class of all unary partial Σ-functions assuming values in the set ω of natural ordinals. We construct a tree T of height 5 such that the hereditarily finite superstructure ℍ(T) over T has no universal Σ-function for the class of all unary partial Σ-functions assuming values 0, 1 only.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    A. N. Khisamiev

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  1. A. N. Khisamiev
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Correspondence to A. N. Khisamiev.

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Translated from Algebra i Logika, Vol. 60, No. 2, pp. 210-230, March-April, 2021. Russian https://doi.org/10.33048/alglog.2021.60.207.

The work was carried out as part of the state assignment to Sobolev Institute of Mathematics SB RAS, project No. 0314-2019-0003.

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Khisamiev, A.N. Universal Functions and Σω-Bounded Structures. Algebra Logic 60, 139–153 (2021). https://doi.org/10.1007/s10469-021-09636-w

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  • DOI: https://doi.org/10.1007/s10469-021-09636-w

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