## 117b – Turing degrees – Lecture 3

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 $\Sigma_n$ 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 $\Sigma_1$ theory of ${\mathcal D}$ is decidable. For this, we will use the technique of forcing to show that there is an infinite set of independent degrees.