My first paper was “An incompleteness theorem for $\beta_n$ models” with Stephen Simpson [1]. It’s a short paper, but the idea is very pretty. We know that the incompleteness theorem implies there are strange models of arithmetic, but these models often seem mysterious, and it’s hard to see what useful properties they can have. But now suppose that a theory of the form $A+B$ meets the hypotheses of the incompleteness theorem, and moreover this theory proves its own consistency, so that $A+B$ is inconsistent. It follows that if $A$ is true (that is, true in the standard model) then $B$ must be false. In this way, we can use the incompleteness theorem to prove facts about the standard model rather than about nonstandard ones. The idea is originally due to Harvey Friedman in his thesis, I believe.

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### Boole’s Rings

- KNAW Academy Colloquium on Generalised Baire Spaces - Lebesgue’s Density Theorem for tree forcing ideals March 22, 2018 [“Sandra Müller”]
- Virtual large cardinal principles at KGRC March 21, 2018 Victoria Gitman
- A model of second-order arithmetic satisfying AC but not DC March 21, 2018 Victoria Gitman
- The universal finite set, Rutgers Logic Seminar, April 2018 March 19, 2018 Joel David Hamkins
- Turin - Combinatorial Variants of Lebesgue’s Density Theorem March 14, 2018 [“Sandra Müller”]

### Comments on Boole’s Rings

- Comment on Upward closure and amalgamation in the generic multiverse of a countable model of set theory by Nonamalgamation in the Cohen generic multiverse, CUNY Logic Workshop, March 2018 | Joel David Hamkins March 22, 2018 Comments for Joel David Hamkins
- Comment on The modal logic of arithmetic potentialism and the universal algorithm by The universal finite set, Rutgers Logic Seminar, April 2018 | Joel David Hamkins March 20, 2018 Comments for Joel David Hamkins
- Comment on The universal finite set by The universal finite set, Rutgers Logic Seminar, April 2018 | Joel David Hamkins March 19, 2018 Comments for Joel David Hamkins
- Comment on How does a slinky fall? by Dave Randell March 15, 2018 Comments for Joel David Hamkins
- Comment on In praise of failure by saf March 13, 2018 Comments for Asaf Karagila