Abstract
AbstractWe 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.
Publisher
Cambridge University Press (CUP)
Reference32 articles.
1. Index sets of quotient objects of the Post numeration;Selivanov;Algebra i Logika,1988
2. Grundlagen der Kombinatorischen Logik
3. Three theorems on recursive enumeration. I. Decomposition. II. Maximal set. III. Enumeration without duplication
4. [5] Barendregt, H. P. and Terwijn, S. A. , Partial combinatory algebra and generalized numberings, preprint, 2019, arXiv:1910.07750.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献