Fri Apr 20, 2007
60 Evans Hall, 4:10–6 PM
Douglas S. Bridges (University of Canterbury)
Constructive Reverse Mathematics
Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Constructive reverse mathematics is reverse mathematics carried out in Bishop-style constructive math (BISH) – that is, using intuitionistic logic and, where necessary, constructive ZF set theory. There are two primary foci of constructive reverse mathematics:
first, investigating which constructive principles are necessary to prove a given constructive theorem;
secondly, investigating what nonconstructive principles are necessary additions to BISH in order to prove a given nonconstructive theorem,
I will present recent work on constructive reverse mathematics, carried out with Josef Berger, Hannes Diener, and Marian Baroni. The main theme of the talk is the connection between the antithesis of Specker’s theorem, various continuity properties, versions of the fan theorem, and Ishihara’s principle BD-N.