Results 1 
2 of
2
The theory of the degrees below 0
 J. London Math. Soc
, 1981
"... Degree theory, that is the study of the structure of the Turing degrees (or degrees of unsolvability) has been divided by Simpson [24; §5] into two parts—global and local. By the global theory he means the study of general structural properties of 3d— the degrees as a partially ordered set or uppers ..."
Abstract

Cited by 18 (6 self)
 Add to MetaCart
Degree theory, that is the study of the structure of the Turing degrees (or degrees of unsolvability) has been divided by Simpson [24; §5] into two parts—global and local. By the global theory he means the study of general structural properties of 3d— the degrees as a partially ordered set or uppersemilattice. The local theory concerns
Notre Dame Journal of Formal Logic Embedding and Coding Below a 1Generic Degree
"... Abstract We show that the theory of D( � g), where g is a 2generic or a 1generic degree below 0 ′ , interprets true first order arithmetic. To this end we show that 1genericity is sufficient to find the parameters needed to code a set of degrees using Slaman and Woodin’s method of coding in Turin ..."
Abstract
 Add to MetaCart
Abstract We show that the theory of D( � g), where g is a 2generic or a 1generic degree below 0 ′ , interprets true first order arithmetic. To this end we show that 1genericity is sufficient to find the parameters needed to code a set of degrees using Slaman and Woodin’s method of coding in Turing degrees. We also prove that any recursive lattice can be embedded below a 1generic degree preserving top and bottom. 1