Abstract
We study a class of permitting arguments in which each positive requirement needs multiple permissions to succeed. Three natural examples of such constructions are given. We introduce a class of r. e. sets, the array nonrecursive sets, which consists of precisely those sets which allow enough permission for these constructions be performed. We classify the degrees of array nonrecursive sets and so classify the degrees in which each of these constructions can be performed.
Keywords
- State Diagram
- Recursive Function
- Peano Arithmetic
- Recursive Approximation
- Dense Simple
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This work was partially supported by National Science Foundation Grants DMS88-00030 to Stob and DMS86-01242 to Jockusch and Downey and also a New Zealand-United States Cooperative Science Program Grant from the National Science Foundation to all three authors. This paper is in final form and no similar paper has been or will be submitted elsewhere.
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Downey, R., Jockusch, C., Stob, M. (1990). Array nonrecursive sets and multiple permitting arguments. In: Ambos-Spies, K., Müller, G.H., Sacks, G.E. (eds) Recursion Theory Week. Lecture Notes in Mathematics, vol 1432. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086116
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DOI: https://doi.org/10.1007/BFb0086116
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