(1/7) Mathematical induction is in some sense the most powerful mathematical technique.

I don't simply mean that it's really useful; I mean that meta-mathematically it often underpins the strength of a foundation. This is the main insight from ordinal analysis.

In addition, many famous theorems from "everyday" mathematics are logically equivalent to induction principles of various strengths. This is the main insight of reverse mathematics.

#MathInduction #Math #Logic #ReverseMathematics

A small survey I wrote on reflection principles in second-order arithmetic is now online. I’ll write a toot sketching _what_ are these reflection principles tonight.

https://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/2228-07.pdf

#Logic #ReverseMathematics