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
Reference43 articles.
1. Askes, M., Downey, R.: Online, computable and punctual structure theory. Log. J. IGPL 08, jzac065 (2022)
2. Ash, C., Knight, J.: Computable structures and the hyperarithmetical hierarchy. Studies in Logic and the Foundations of Mathematics, vol. 144. North-Holland Publishing Co., Amsterdam (2000)
3. Alaev, P.E.: Existence and uniqueness of structures computable in polynomial time. Algebra Log. 55(1), 72–76 (2016)
4. Alaev, P.E.: Categoricity for primitively recursive and polynomial Boolean algebras. Algebra Log. 57(4), 389–426 (2018)
5. Alaev, P.E.: Finitely generated structures computable in polynomial time. Sib. Math. J. 63(5), 801–818 (2022)