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Manfred comments on Mathematics for AIXI and Gödel machine - Less Wrong Discussion
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The things you directly need are algorithmic complexity theory (Classic textbook: Li and Vitanyi) and some way of understanding proofs (Probably start with regular mathematical logic / model theory, not sure of a standout textbook here, maybe Manin?, then look into modal logic, classic textbook by Boolos).
Prerequisites for those are mathematical logic, set theory, probability theory, and some amount of discrete math.
Thank you, I'm grateful for your time.