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computable sets and functions, Turing degrees, c.e. degrees, models of computability, primitive recursion, oracle computation, models of computability, decision problems, undecidability, Turing jump, halting problem, notions of computable randomness, computable model theory, computable equivalence relation theory, arithmetic and hyperarithmetic hierarchy, infinitary computability, $\alpha$-recursion, complexity theory.

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Kolmogorov Complexity and Proof Techniques

Using the same technique, one can construct infinitely many statements which are true with probability arbitrarily close to 1, but are nonetheless unprovable. See lemma 4 in http://theory.stanford.edu …
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