Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Perfect Local Computability and Computable Simulations
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Real Computable Manifolds and Homotopy Groups
UC '09 Proceedings of the 8th International Conference on Unconventional Computation
| Hi-index | 0.00 |
We introduce the notion of a locally computable structure, a natural way of generalizing the notions of computable model theory to uncountable structures ${\mathcal{S}}$ by presenting the finitely generated substructures of $\S$ effectively. Our discussion emphasizes definitions and examples, but does prove two significant results. First, our notion of m-extensional local computability of ${\mathcal{S}}$ ensures that the Σn-theory of ${\mathcal{S}}$ will be Σnfor all n≤ m+ 1. Second, our notion of perfect local computability is equivalent (for countable structures) to the classic definition of computable presentability.