Punctually presented structures II: comparing presentations

Archive for Mathematical Logic 64 (1):159-184 (2025)
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Abstract

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 ( Z,<\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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Alexander Melnikov
National Research University Higher School of Economics

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