Doing mathematics in J_2

Michael Rathjen, University of Leeds. Part of the proofs, constructions and computations seminar series.

We are all familiar with the claim of Reverse Mathematics that "Ordinary Mathematics" can be developed in fairly weak background theories. The coding of mathematics in fragments of second order arithmetic, as done in Reverse Mathematics, is a bit awkward, though. Also dissenting voices flare up now and then. So I thought it would be interesting to see what an expert in functional analysis, who also knows the mathematics needed for physics, has to say about it. Nick Weaver has two  papers on developing mathematics in proof-theoretically weak theories. One develops mathematics in a small set-theoretic world known as Jensen's J_2. The other paper looks at mathematics from the viewpoint of third order arithmetic. It'll be interesting to gauge the proof-theoretic strength of the latter.