Article contents
COMPUTABILITY IN PARTIAL COMBINATORY ALGEBRAS
Published online by Cambridge University Press: 05 January 2021
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.
- Type
- Articles
- Information
- Creative Commons
- This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Copyright
- © The Author(s), 2021. Published by Cambridge University Press
References
REFERENCES
- 1
- Cited by