Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Electronic Notes in Theoretical Computer Science (ENTCS)
A Brief Critique of Pure Hypercomputation
Minds and Machines
| Hi-index | 0.00 |
Computability theory, which investigates computable functions and computable sets, lies at the foundation of computer science. Its classical presentations usually involve a fair amount of Godel encodings which sometime obscure ingenious arguments. Consequently, there have been a number of presentations of computability theory that aimed to present the subject in an abstract and conceptually pleasing way. We build on two such approaches, Hyland's effective topos and Richman's formulation in Bishop-style constructive mathematics, and develop basic computability theory, starting from a few simple axioms. Because we want a theory that resembles ordinary mathematics as much as possible, we never speak of Turing machines and Godel encodings, but rather use familiar concepts from set theory and topology.