Feferman's Forays into the Foundations of Category Theory

• 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.

Ämnesord

HUMANIORA  -- Filosofi, etik och religion -- Filosofi (hsv//swe)

HUMANITIES  -- Philosophy, Ethics and Religion -- Philosophy (hsv//eng)

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

Nyckelord

Category theory

Stratified set theory

Zermelo-Fraenkel set theory

Small/large distinction

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