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Feferman's Forays into the Foundations of Category Theory

Chapter in book
Authors Ali Enayat
Paul Kindvall Gorbow
Zachiri McKenzie
Published in Feferman on Foundations / Jaeger, Gerhard, Sieg, Wilfried (Eds.)
Pages 315-346
ISBN 978-3-319-63332-9
ISSN 2211-2758
Publisher Springer International Publishing
Place of publication Cham
Publication year 2017
Published at Department of Philosophy, Linguistics and Theory of Science
Pages 315-346
Language en
Links https://doi.org/10.1007/978-3-319-6...
Keywords Category theory, Stratified set theory, Zermelo-Fraenkel set theory, Small/large distinction
Subject categories Mathematical logic, Logic

Abstract

The foundations of category theory has been a source of many perplexities ever since the groundbreaking 1945-introduction of the subject by Eilenberg and Mac Lane; e.g., how is one to avoid Russell-like paradoxes and yet have access to objects that motivate the study in the first place, such as the category of all groups, or the category of all topological spaces? Solomon Feferman has grappled with such perplexities for over 45 years, as witnessed by his six papers on the subject during the period 1969-2013. Our focus in this paper is on two important, yet quite different set-theoretical systems proposed by Feferman for the implementation of category theory: the ZF-style system ZFC/S and the NFU-style system S*; where NFU is Jensen's urelemente-modication of Quine's New Foundations system NF of set theory.

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