From sets and types to topology and analysis towards practicable foundations for constructive mathematics (book review)

Abstract

This book reminded me of another collection of papers, also co-edited by Peter Schuster: Reuniting the antipodes-constructive and nonstandard views on the continuum, Kluwer, 2001. It brought together various non-classical approaches to Analysis. When I reviewed this book for Nieuw Archief voor Wiskunde I naturally raised the question: have the antipodes been reunited? Of course the answer was no: with few exceptions (most notably Erik PalmgrenÕs contribution), the authors stayed Þrmly within their specialism. A similar reuniÞcation project has led to the present book: like the Reuniting volume, it is also the proceedings of a workshop in Venice, this one from 2003. And in this case the 'antipodes' are the students of formal foundational systems (and their semantics) on the one hand, and the 'practicioners', the researchers doing 'constructive mathematics' on the other.