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Set Theory and Structures

Barton, Neil and Friedman, Sy-David (2019) Set Theory and Structures. [Preprint]

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Abstract

Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that fruitfully interrelates a `structural' perspective to a set-theoretic one. We present a set-theoretic system that is able to talk about structures more naturally, and argue that it provides an important perspective on plausibly structural properties such as cardinality. We conclude the language of set theory can provide useful information about the notion of mathematical structure.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Barton, Neilbartonna@gmail.com0000-0002-3637-1730
Friedman, Sy-David
Keywords: set theory, category theory, urelement, structuralism
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Methodology
Specific Sciences > Mathematics
Depositing User: Dr. Neil Barton
Date Deposited: 15 Apr 2019 18:11
Last Modified: 15 Apr 2019 18:11
Item ID: 15908
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Methodology
Specific Sciences > Mathematics
Date: 2019
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/15908

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