K. J. Khoo, H. T. Koh, K. M. Ng. A discrete linear order with non-dense punctual degrees . Theoretical Computer Science, vol. 1047 (2025), Paper no. 115324, 20 pp. - N. Bazhenov, K. M. Ng, L. S. Mauro, A. Sorbi. Primitive recursive equivalence relations and their primitive recursive complexity . Computability, vol.11, nos. 3-4 (2022), pp. 187–221. - B. S. Kalmurzayev, N. A. Bazhenov, A. M. Iskakov. Computably enumerable equivalence relations via primitive recursive reductions , Journal of Logic and Computation, vol. 35, no. 2 (2024), Paper no. exad082, 31 pp.

Ellen Hammatt

doi:10.1017/bsl.2026.10155

April 24, 2026Bulletin of Symbolic Logic

K. J. Khoo, H. T. Koh, K. M. Ng. A discrete linear order with non-dense punctual degrees . Theoretical Computer Science, vol. 1047 (2025), Paper no. 115324, 20 pp. - N. Bazhenov, K. M. Ng, L. S. Mauro, A. Sorbi. Primitive recursive equivalence relations and their primitive recursive complexity . Computability, vol.11, nos. 3-4 (2022), pp. 187–221. - B. S. Kalmurzayev, N. A. Bazhenov, A. M. Iskakov. Computably enumerable equivalence relations via primitive recursive reductions , Journal of Logic and Computation, vol. 35, no. 2 (2024), Paper no. exad082, 31 pp.

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Key Points

The aim is to explore discrete linear orders with non-dense punctual degrees and classify primitive recursive equivalence relations.
Theoretical frameworks implemented to demonstrate conditions of non-dense punctual degrees.
Analysis of primitive recursive equivalence relations using complexity metrics.
Utilization of computably enumerable relations through primitive recursive reductions.
Establishment of properties for discrete linear orders exhibiting non-dense punctual degrees.
Characterization of primitive recursive equivalence relations with clear complexity classifications.
Evidence showing the role of reductions in comprehensible enumerable equivalence relations.

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Implication

Theoretical work investigates non-dense punctual degrees in discrete orders, impacting equivalence relations.

Abstract

K. J. Khoo, H. T. Koh, K. M. Ng. A discrete linear order with non-dense punctual degrees. Theoretical Computer Science, vol. 1047 (2025), Paper no. 115324, 20 pp. - N. Bazhenov, K. M. Ng, L. S. Mauro, A. Sorbi. Primitive recursive equivalence relations and their primitive recursive complexity. Computability, vol.11, nos. 3-4 (2022), pp. 187–221. - B. S. Kalmurzayev, N. A. Bazhenov, A. M. Iskakov. Computably enumerable equivalence relations via primitive recursive reductions, Journal of Logic and Computation, vol. 35, no. 2 (2024), Paper no. exad082, 31 pp.

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Ellen Hammatt (2026) studied this question.

synapsesocial.com/papers/69edad6b4a46254e215b5021 https://doi.org/10.1017/bsl.2026.10155

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