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  Sn 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.

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