Author : Richard Warren Blaylock
Release : 1991
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Some Results One-genericity and Recursively Enumerable Weak Truth Table Degrees by : Richard Warren Blaylock
Download or read book Some Results One-genericity and Recursively Enumerable Weak Truth Table Degrees written by Richard Warren Blaylock. This book was released on 1991. Available in PDF, EPUB and Kindle. Book excerpt: In this manuscript we explore two topics in recursion theory and their interaction. The first topic is e-genericity, a notion of genericity for recursively enumerable (r.e.) sets introduced by C. G. Jockusch, Jr. The second is weak truth table reducibility (w-reducibility), a strong reducibility (i.e., stronger than the most general Turing reducibility) first introduced by Friedberg and Rogers. In Chapter 1 we give a brief introduction to these topics and establish the relevant terminology and notation. In Chapter 2 we give some closure and non-closure properties for the classes of e-generic sets and degrees, which are predicted by analogous results for previous notions of genericity. For example, the e-generic sets are not closed under union, intersection, or join, but on the other hand if the join $A oplus B$ of two sets is e-generic, then so are $A,B, A cup B$, and $A cap B$. In Chapter 3 we investigate the structure of the weak truth table degrees (w-degrees) inside an e-generic Turing degree. Here we show that e-generic Turing degrees are highly noncontiguous in the sense that they contain no greatest and no least r.e. w-degree. Finally in Chapter 4 we obtain some results on the ordering of the r.e. w-degrees in general. The main result is the existence of a nontrivial r.e. w-degree a which has a greatest lower bound with every r.e. w-degree b. We also show that these nontrivial completely cappable degrees can neither be low nor promptly simple.
