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 S_{1} 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), 369389.
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