Universal Functions and KΣ-Structures

Abstract

We introduce the concept of KΣ-structure and prove the existence of a universal Σ-function in the hereditarily finite superstructure over this structure. We exhibit some examples of families of KΣ-structures of the theory of trees.

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Acknowledgment

The author is grateful to S. S. Goncharov for stating the problem and giving useful advice.

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Correspondence to A. N. Khisamiev.

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Dedicated to the outstanding mathematician Yuri Leonidovich Ershov on the occasion of his 80th birthday.

Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 3, pp. 703–716.

The author was funded within the Government Task to the Sobolev Institute of Mathematics (Project 0314-2019-0003).

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Khisamiev, A.N. Universal Functions and KΣ-Structures. Sib Math J 61, 552–562 (2020). https://doi.org/10.1134/S0037446620030192

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Keywords

  • hereditarily finite superstructure
  • universal Σ-function
  • KΣ-structure
  • tree