Douglas S. Bridges

2. May 2016

Morse Set Theory as a Foundation for Constructive Mathematics

In the northern autumn of 1972, I came across A.P. Morse’s little book ‘A Theory of Sets’, and became absorbed by the idea of carrying through a constructive development of set theory (CMST) along the same lines, in which everything was expressed in a kind of pseudocode governed by strict rules of language and notation. Such a development would seem to be particularly suitable for the extraction of programs from proofs and for their subsequent implementation.

Chapter 1 of my D.Phil. thesis (Oxford, 1974) contained the fruits of my labours to that stage. After that, despite a brief foray into CMST for a conference paper in 1986, my plan to develop the set theory in greater depth was shelved until taken up again in the autumn of 2013.

In this talk I sketch some of the salient features of the substantially updated development of CMST over the last two-and-a-half years, paying particular attention to where the constructive theory deviates from Morse’s classical counterpart and to those results of the latter that are essentially nonconstructive.