## Natural Definability in Degree Structures (0)

Citations: | 5 - 1 self |

### BibTeX

@MISC{Shore_naturaldefinability,

author = {Richard A. Shore},

title = {Natural Definability in Degree Structures},

year = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

. A major focus of research in computability theory in recent years has involved denability issues in degree structures. There has been much success in getting general results by coding methods that translate rst or second order arithmetic into the structures. In this paper we concentrate on the issues of getting denitions of interesting, apparently external, relations on degrees that are order-theoretically natural in the structures D and R of all the Turing degrees and of the r.e. Turing degrees, respectively. Of course, we have no formal denition of natural but we oer some guidelines, examples and suggestions for further research. 1. Introduction A major focus of research in computability theory in recent years has involved denability issues in degree structures. The basic question is, which interesting apparently external relations on degrees can actually be dened in the structures themselves, that is, in the rst order language with the single fundamental relation...