journal article Mar 01, 1966

On the indexing of classes of recursively enumerable sets

Abstract
In this paper we follow up our work in [2] on standard classes of recursively enumerable sets, and it will be supposed that the reader is familiar with [2]. One of the main problems left open in [2], that of determining whether or not every standard class has a least member is resolved by the construction of a standard class all of whose members are non-empty, and two of whose members are disjoint. This shows that there is a standard class which is not p.r. in the sense of [2] and we now prefer the adjective sequential for those standard classes which were called p.r. in [2]. Otherwise our terminology will be the same as in [2]. We shall also prove the theorem only stated in [2] that any standard class all of whose members have cardinality < 3 is sequential. Further, we give an example of a standard class which is not sequential and all of whose members have cardinality < 4.
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Metrics
16
Citations
3
References
Details
Published
Mar 01, 1966
Vol/Issue
31(1)
Pages
10-22
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Cite This Article
A. H. Lachlan (1966). On the indexing of classes of recursively enumerable sets. The Journal of Symbolic Logic, 31(1), 10-22. https://doi.org/10.2307/2270617
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