Please use this identifier to cite or link to this item: https://doi.org/10.1007/978-3-642-03073-4_28
Title: Index sets and universal numberings
Authors: Jain, S. 
Stephan, F. 
Teutsch, J.
Issue Date: 2009
Citation: Jain, S.,Stephan, F.,Teutsch, J. (2009). Index sets and universal numberings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 5635 LNCS : 270-279. ScholarBank@NUS Repository. https://doi.org/10.1007/978-3-642-03073-4_28
Abstract: This paper studies the Turing degrees of various properties defined for universal numberings, that is, for numberings which list all partial-recursive functions. In particular properties relating to the domain of the corresponding functions are investigated like the set DEQ of all pairs of indices of functions with the same domain, the set DMIN of all minimal indices of sets and DMIN 1 of all indices which are minimal with respect to equality of the domain modulo finitely many differences. A partial solution to a question of Schaefer is obtained by showing that for every universal numbering with the Kolmogorov property, the set DMIN1 is Turing equivalent to the double jump of the halting problem. Furthermore, it is shown that the join of DEQ and the halting problem is Turing equivalent to the jump of the halting problem and that there are numberings for which DEQ itself has 1-generic Turing degree. © 2009 Springer Berlin Heidelberg.
Source Title: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
URI: http://scholarbank.nus.edu.sg/handle/10635/113936
ISBN: 3642030726
ISSN: 03029743
DOI: 10.1007/978-3-642-03073-4_28
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