Seminario: Morse Set Theory as a Foundation for Constructive Mathematics

Giovedì 8 Maggio 2014, ore 16:30 - Sala Riunioni VII Piano - Douglas Bridges


Giovedì 8 Maggio 2014 alle ore 16:30 in Sala Riunioni al VII Piano della Torre Archimede, Douglas Bridges (Department of Mathematics and Statistics, University of Canterbury, New Zealand) terrà un seminario dal titolo "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 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 late last year.
In this talk I sketch some of the salient features of this updated development of CMST, paying particular attention to where it deviates from Morse's classical theory and to those results of the latter that are essentially nonconstructive.