Part 2. Computability Theory: Very Powerful Models 15 7. Turing Machines: 1/28/14 15 8. Recognizability, Decidability, and Reductions: 1/30/14 18 9. Reductions, Undecidability, and the Post Correspondence Problem: 2/4/14 21 10. Oracles, Rice’s Theorem, the Recursion Theorem, and the Fixed-Point Theorem: 2/6/14 23 11. Self-Reference and the Foundations of Mathematics: 2/11/14 26 12. A Universal ...