We presented a general framework for forcing arguments, and gave the proof of the existence of incomparable degrees in the language of forcing.
We defined the hierarchy of formulas and defined theories, the theory of a structure, and what it means for a theory to be decidable.
We want to show that the theory of is decidable. For this, we will use the technique of forcing to show that there is an infinite set of independent degrees.
Degree structures: local and global investigations, by R. Shore. Bulletin of Symbolic Logic 12 (3) (2006), 369-389.