Godel's Incompleteness
Chaitin’s Incompleteness theorem
Related to the Surprise Paradox:
- http://www.wisdom.weizmann.ac.il/mathusers/ranraz/publications/Pincompleteness.pdf
- The Surprise Examination Paradox and the Second Incompleteness Theorem
- http://math.ucr.edu/home/baez/surprises.html