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FOUNDATIONS OF UNLIMITED CATEGORY THEORY: WHAT REMAINS TO BE DONE

Published online by Cambridge University Press:  01 June 2012

SOLOMON FEFERMAN
SOLOMON FEFERMAN*
Affiliation:
Department of Mathematics, Stanford University
*
*DEPARTMENT OF MATHEMATICS, STANFORD UNIVERSITY, STANFORD, CA 94305 E-mail: [email protected]
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Abstract

Following a discussion of various forms of set-theoretical foundations of category theory and the controversial question of whether category theory does or can provide an autonomous foundation of mathematics, this article concentrates on the question whether there is a foundation for “unlimited” or “naive” category theory. The author proposed four criteria for such some years ago. The article describes how much had previously been accomplished on one approach to meeting those criteria, then takes care of one important obstacle that had been met in that approach, and finally explains what remains to be done if one is to have a fully satisfactory solution.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 6 , Issue 1 , March 2013 , pp. 6 - 15
Copyright
Copyright © Association for Symbolic Logic 2012

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