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Abstract <p>In 1998, R. Downey raised the question of describing the properties of order <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(P\)</EquationSource> <!--RusMath2570081Zubkov-m1--> </InlineEquation> such that for any low linear order <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L\)</EquationSource> <!--RusMath2570081Zubkov-m2--> </InlineEquation> if <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(P(L)\)</EquationSource> <!--RusMath2570081Zubkov-m3--> </InlineEquation> holds, then <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(L\)</EquationSource> <!--RusMath2570081Zubkov-m4--> </InlineEquation> 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.</p>

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A Low Scattered Linear Order of Rank 2 without Computable Copy

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • M. V. Zubkov

摘要

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.