Computability of Distributive Lattices

N. A. Bazhenov, A. N. Frolov, I. Sh Kalimullin, A. G. Melnikov

Результат исследования: Научные публикации в периодических изданияхстатья

2 Цитирования (Scopus)

Аннотация

The class of (not necessarily distributive) countable lattices is HKSS-universal, and it is also known that the class of countable linear orders is not universal with respect to degree spectra neither to computable categoricity. We investigate the intermediate class of distributive lattices and construct a distributive lattice with degree spectrum {d: d ≠ 0}. It is not known whether a linear order with this property exists. We show that there is a computably categorical distributive lattice that is not relatively Δ2 0-categorical. It is well known that no linear order can have this property. The question of the universality of countable distributive lattices remains open.

Язык оригиналаанглийский
Страницы (с-по)959-970
Число страниц12
ЖурналSiberian Mathematical Journal
Том58
Номер выпуска6
DOI
СостояниеОпубликовано - 1 ноя 2017

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  • Цитировать

    Bazhenov, N. A., Frolov, A. N., Kalimullin, I. S., & Melnikov, A. G. (2017). Computability of Distributive Lattices. Siberian Mathematical Journal, 58(6), 959-970. https://doi.org/10.1134/S0037446617060052