Punctually presented structures II: comparing presentations

Author:

Dorzhieva Marina,Downey Rodney,Hammatt Ellen,Melnikov Alexander G.,Ng Keng Meng

Abstract

AbstractWe 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.

Funder

Rutherford Discovery

Marsden Fund

Victoria University of Wellington

Publisher

Springer Science and Business Media LLC

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