GENERALIZED NUMBERING FOR LINEAR ORDERS
СЫЗЫҚТЫҚ РЕТТЕР ҮШІН ЖАЛПЫ НӨМІРЛЕУЛЕР
ОБОБЩЕННАЯ НУМЕРАЦИЯ ДЛЯ ЛИНЕЙНЫХ ПОРЯДКОВ
Issakhov A.A. Kalmurzayev B.S. Rakymzhankyzy F.
2025Kazakh-British Technical University
Herald of the Kazakh British Technical UNiversity
2025#22Issue 2200 - 206 pp.
We study spectre of Turing degrees permitting to construct numbeings for the set of all linear orders isomorphic to the standard order of natural numbers. It is known that the index set of all linear orders isomorphic to the standard order of natural numbers is-comlete. This mean that this set has no computable numberings. In this work we show that the set of all linear orders isomorphic to the standard order of naturals has-computable numbering, and has no-computable numberings. In the Bazhenov, Kalmurzayev and Torebekova’s work they construct universal c.e. linear preorder in the structure under computably reducibility. They use the following fact: there is computable numbering for some subset of c.e. linear preorders such that any c.e. linear preorder lies in lower cone for some c.e. linear order from . We show that the similar fact is not hold for the structure of all linear orders isomorphic to the standard order of naturals. Moreover, for this structure there is no-computable numbering with simiral fact.
computable reducibility , positive equivalence , positive linear preorder , positive preorder
Text of the article Перейти на текст статьи
Kazakh-British Technical University, Almaty, Kazakhstan
International Information Technology University, Almaty, Kazakhstan
Al-Farabi Kazakh National University, Almaty, Kazakhstan
Kazakh-British Technical University
International Information Technology University
Al-Farabi Kazakh National University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026