# Morse Set Theory as a Foundation for Constructive Mathematics

**Date**: Wednesday 28 June 2017, 14:00 – 15:30**Location**: Mathematics Level 8, MALL 1 & 2, School of Mathematics**Type**: Proofs, Constructions and Computations, Seminars, Pure Mathematics**Cost**: Free

#### Douglas Bridges, University of Canterbury. Part of the proofs, constructions and computations seminar series.

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 subsequence 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 three-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.

**Douglas Bridges,** *University of Canterbury*