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.



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Quinn, thank you for doing this! I just looked through the first post and it's very nice and clear. Maybe Patrick and Paul can comment on the other two.

Thanks for the nice comment. I listed the PD post first, as it is probably the most readable of the three, written more like an article than like notes.

Sorry to be late to the party, but that's a really excellent write-up of the Robust Cooperation paper! Thanks for doing this.