Abstract.
A Cantor singleton is the unique nonrecursive member of some \(\Pi^0_1\) class. In this paper we investigate the relationships between the following three notions: Cantor singletons, Cantor-Bendixson rank, and recursive join. Among other results, we show that the rank of \(A\oplus B\) is at most the natural sum of the ranks of \(A\) and \(B\), and that, if \(B\) has the same rank as \(A\o plus B\), then \(A\) is recursive in \(B\).
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received August 1, 1994
Rights and permissions
About this article
Cite this article
Owings, J. Rank, join, and Cantor singletons . Arch Math Logic 36, 313–320 (1997). https://doi.org/10.1007/s001530050068
Issue Date:
DOI: https://doi.org/10.1007/s001530050068