117b – Turing degrees – Lecture 3

We present a general framework for forcing arguments, and give the proof of the existence of incomparable degrees in the language of forcing.

We define the hierarchy of  S_n formulas and define theories, the theory of a structure, and what it means for a theory to be decidable.

We want to show that the S₁ theory of D is decidable. For this, we will use the technique of forcing to show that there is an infinite set of independent degrees.

Additional reference:

• Degree structures: local and global investigations, by R. Shore. Bulletin of Symbolic Logic 12 (3) (2006), 369-389.

Advertisements