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Structures of Degrees of Negative Representations of Linear Orders

Abstract

The structures of partially ordered sets of degrees of negative and positive representability of linear orders are studied. The focus is on the negative representability of linear orders and orders with endomorphisms. In particular, for these structures, we established the existence of incomparable, maximal, and minimal degrees, infinite chains and anti-chains, and also considered the connection with the concepts of the reducibility of enumerartions, splittable degrees and positive representations.

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Funding

This work was financially supported by the Heritage of Academician T.N. Kara–Niyazov Foundation.

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Correspondence to N. Kh. Kasymov, R. N. Dadazhanov or S. K. Djavliev.

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Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 12, pp. 31–55.

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Kasymov, N.K., Dadazhanov, R.N. & Djavliev, S.K. Structures of Degrees of Negative Representations of Linear Orders. Russ Math. 65, 27–46 (2021). https://doi.org/10.3103/S1066369X21120045

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  • DOI: https://doi.org/10.3103/S1066369X21120045

Keywords

  • linear order with endomorphisms
  • enumerated system
  • negative and positive representations
  • degree of representability
  • standard representation
  • splittable degree.