A Low Scattered Linear Order of Rank 2 without Computable Copy

In 1998, R. Downey raised the question of describing the properties of order $$P$$ such that for any low linear order $$L$$ if $$P(L)$$ holds, then $$L$$ has a computable copy. This paper shows that scattering is not such a property. Namely, a low scattered linear order of rank 2 with no computable copy is constructed.

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Publication Details

Journal
Russian Mathematics
Published
2025-10-01
DOI
https://doi.org/10.3103/s1066369x25700811
Primary Topic
Computability, Logic, AI Algorithms
Type
article
Field-Weighted Citation Impact
0.00
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article

A Low Scattered Linear Order of Rank 2 without Computable Copy

M. V. Zubkov
Russian Mathematics
Computability, Logic, AI Algorithms
article

A Low Scattered Linear Order of Rank 2 without Computable Copy

M. V. Zubkov
article en

Abstract

In 1998, R. Downey raised the question of describing the properties of order $$P$$ such that for any low linear order $$L$$ if $$P(L)$$ holds, then $$L$$ has a computable copy. This paper shows that scattering is not such a property. Namely, a low scattered linear order of rank 2 with no computable copy is constructed.

Russian MathematicsVol. 69(10)
Kazan Federal University (RU)
Openalex Percentile: Top 24%
Computability, Logic, AI Algorithms
DOISourceOpenAlex
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A Low Scattered Linear Order of Rank 2 without Computable Copy — M. V. Zubkov · Russian Mathematics (2025) | TGRS Research Map | TGRS