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TOWARD A MINIMALIST FOUNDATION FOR CONSTRUCTIVE MATHEMATICS

Maria Emilia Maietti and Giovanni Sambin

in From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566519
eISBN:
9780191713927
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566519.003.0006
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

The two main views in modern constructive mathematics usually associated with constructive type theory and topos theory are compatible with the classical view, but they are incompatible with each ... More


SOME CONSTRUCTIVE ROADS TO TYCHONOFF

Steven Vickers

in From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566519
eISBN:
9780191713927
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566519.003.0014
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter discusses the Tychonoff Theorem with respect to point-free topology from the point of view of both topos-valid and predicative mathematics. A new proof of the infinitary Tychonoff ... More


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