Understand Yates index set theorem as a statement about the foursome, and relate it to the Yoneda lemma.

Study

• Find good video courses about computability.
• Write down all the examples of sets in the arithmetic hierarchy as prenex statements.
• Intuit from these examples how they express the power of their level.
• Study from Soare Chapter IV how to demonstrate that they are not less than that level.
• Think about the general form of the matrix of a prenex statement (which is quantifiers plus a matrix).
• Understand Sutner's remark that existence can be thought of as geometric projection. How does that relate to perspectives?
• Study Soare Chapter XII.

Questions

• In this context, what is a perspective?
• Consider whether there is a connection between the automata hierarchy and Bott periodicity.
• Relate the quantifiers in the sevensome/eightsome with the arithmetical hierarchy and the foursome, how four levels yield the three-cycle upon identifying the first and the last levels, the null level with consciousness of the null level.
• Express nondeterminism and determinism in terms of universal and existential quantifiers, respectively.