Пунктуальные Копии Алгебраических Структур

Zubkov, M. V.; Kalimullin, I. Sh.; Melnikov, Alexander G.; Frolov, A. N.

doi:10.33048/smzh.2019.60.607

Sib. Mat. Zh.

2019

DOI: 10.33048/smzh.2019.60.607

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Пунктуальные Копии Алгебраических Структур

M. V. Zubkov¹,

I. Sh. Kalimullin²,

Alexander G. Melnikov³

et al.

Abstract: Аннотация. Оценивается сложность построения пунктуальной онлайн копии алгебраической структуры. Установлены общая верхняя оценка, а также оптимальные оценки для классов булевых алгебр, абелевых p-групп и линейных порядков. Кроме того, развитые здесь методы применяются для решения открытой проблемы Монталбана (2013) о копируемых линейных порядках.

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Punctually presented structures II: comparing presentations

Dorzhieva,

Downey,

Hammatt

et al. 2024

Arch. Math. Logic

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We investigate the problem of punctual (fully primitive recursive) presentability of algebraic structures up to primitive recursive and computable isomorphism. We show that for mono-unary structures and undirected graphs, if a structure is not punctually categorical then it has infinitely many punctually non-isomorphic punctual presentations. We also show that the punctual degrees of any computably almost rigid structure as well as the order ($$\mathbb {Z},<$$ Z , < ) are dense. Finally we characterise the Boolean algebras which have a punctually 1-decidable presentation that is computably isomorphic to a 1-decidable presentation.

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Punctually presented structures II: comparing presentations

Dorzhieva,

Downey,

Hammatt

et al. 2024

Arch. Math. Logic

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show abstract

Punctually presented structures I: Closure theorems

Dorzhieva,

Melnikov

2023

COM

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Пунктуальные Копии Алгебраических Структур

Cited by 2 publications

References 13 publications

Punctually presented structures II: comparing presentations

Punctually presented structures II: comparing presentations

Punctually presented structures I: Closure theorems

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