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

- Consistency strength lower bounds for the proper forcing axiom via the core model induction March 5, 2020 Sandra Müller
- Logic Colloquium Poznan - TBA March 5, 2020 Sandra Müller
- North American Annual Meeting of the ASL - How to obtain lower bounds in set theory March 4, 2020 Sandra Müller
- International Day of Mathematics, Vienna - Das Unbegreifliche verstehen - die Faszination Unendlichkeit March 3, 2020 Sandra Müller
- The real numbers are not interpretable in the complex field February 24, 2020 Joel David Hamkins

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