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Computability in partial combinatory algebras
Published 21 Oct 2019 in math.LO and cs.LO | (1910.09258v3)
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.
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