I've been learning math lately; specifically I've been reading MIRI's recent research preprints and the prerequisite material. In order to actually learn math, I typically have to write it down again, usually with more details and context. I started a blog to make my notes on these papers public, and I think they're of high enough quality that I ought to share them here.
Note: my use of the pronoun "we" is instilled habit; I am not claiming to have helped develop the core ideas herein.
- Löb's Theorem and the Prisoner's Dilemma is an account of the LaVictoire et al paper Robust Cooperation in the Prisoner's Dilemma.
- Details in Provability Logic is a technical followup to the above, which goes into the details of modal logic needed for the LaVictoire et al paper; namely the normal form theorem, the fixed point theorem, and the decidability of GL via Kripke semantics.
- Definability of Truth in Probabilistic Logic goes through the Christiano et al paper of the same name. It's a little rougher around the edges on account of being the first blog post I ever wrote (and being produced more hastily than the other two). I note that the construction doesn't truly require the Axiom of Choice.