Morse Set Theory as a Foundation for Constructive Mathematics

Speaker:  Douglas S. Bridges - University of Canterbury, Christchurch, New Zealand
  Wednesday, March 2, 2016 at 5:00 PM Seminario di Logica
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.


Programme Director
Margherita Zorzi

Publication date
April 25, 2016