Computability in partial combinatory algebras
Logic
2020-02-06 v3 Logic in Computer Science
Abstract
We prove a number of elementary facts about computability in partial combinatory algebras (pca's). We disprove a suggestion made by Kreisel about using Friedberg numberings to construct extensional pca's. We then discuss separability and elements without total extensions. We relate this to Ershov's notion of precompleteness, and we show that precomplete numberings are not 1-1 in general.
Cite
@article{arxiv.1910.09258,
title = {Computability in partial combinatory algebras},
author = {S. A. Terwijn},
journal= {arXiv preprint arXiv:1910.09258},
year = {2020}
}