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Abstract <p>One of the central themes in the computable theory of linear orders is determining which low orders are computably presentable. This, in turn, raises the question of which order properties guarantee a computable copy for any low order. In this paper, we investigate the property of being scattered by constructing a counterexample: a low scattered linear order of Hausdorff rank 2 that has no computable copy. This construction provides such a counterexample of minimal finite rank.</p>

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On a Low Scattered Linear Order with no Computable Copy

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • M. V. Zubkov

摘要

Abstract

One of the central themes in the computable theory of linear orders is determining which low orders are computably presentable. This, in turn, raises the question of which order properties guarantee a computable copy for any low order. In this paper, we investigate the property of being scattered by constructing a counterexample: a low scattered linear order of Hausdorff rank 2 that has no computable copy. This construction provides such a counterexample of minimal finite rank.