Ingrassia proved that the p-generic Turing degrees are dense in the r.e. degrees and Ding De-cheng proved that the non-p-generic degrees are dense in the r.e. degrees too. But, do these two kinds of degrees have the s...Ingrassia proved that the p-generic Turing degrees are dense in the r.e. degrees and Ding De-cheng proved that the non-p-generic degrees are dense in the r.e. degrees too. But, do these two kinds of degrees have the same frequency of occurrency in every part of the r.e. degrees? In this note we give a negative answer.展开更多
In this paper, we prove that every p-generic r.e. degree is noncontiguous, and then, by the density of p-generic degrees, the noncontiguous degrees are dense in the r.e. degrees.
基金Project supported by the National Natural Science Foundation of China.
文摘Ingrassia proved that the p-generic Turing degrees are dense in the r.e. degrees and Ding De-cheng proved that the non-p-generic degrees are dense in the r.e. degrees too. But, do these two kinds of degrees have the same frequency of occurrency in every part of the r.e. degrees? In this note we give a negative answer.
基金Project supported by the National Natural Science Foundation of China and by a Grant by the Volkswagen Foundation of Germany for a Chinese-German Binational Research Project in Recursion Theory and Complexity Theory
文摘In this paper, we prove that every p-generic r.e. degree is noncontiguous, and then, by the density of p-generic degrees, the noncontiguous degrees are dense in the r.e. degrees.
