论文信息 - The minimum degree of recursively representable choice functions

The minimum degree of recursively representable choice functions

Abstract We show that the minimum degree of Turing complexity of a recursively representable choice function is O″, the degree of a complete ∑ 2 set in the Kleene-Mostowski hierarchy. A consequence of this result is that the complexity of such choice functions in this sense is bounded strictly above the degrees of R.E. subsets on N .

Alain A. Lewis

[1] Joseph R. Shoenfield,et al. Degrees of unsolvability , 1959, North-Holland mathematics studies.

[2] Walter J. Savitch,et al. The Turing Degree of the Inherent Ambiguity Problem for Context-Free Languages , 1975, Theor. Comput. Sci..

[3] Jr. Hartley Rogers. Theory of Recursive Functions and Effective Computability , 1969 .

[4] A. A. Lewis,et al. On effectively computable realizations of choice functions : Dedicated to Professors Kenneth J. Arrow and Anil Nerode , 1985 .

[5] Emil L. Post. Recursively enumerable sets of positive integers and their decision problems , 1944 .

[6] G. Sacks. Degrees of unsolvability , 1965 .

[7] Emil L. Post,et al. The Upper Semi-Lattice of Degrees of Recursive Unsolvability , 1954 .

[8] J. C. Shepherdson,et al. Utility theory based on rational probabilities , 1980 .

[9] S. Kleene. Recursive predicates and quantifiers , 1943 .