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Rethinking Set Theory

Tom Leinster
The American Mathematical Monthly
Vol. 121, No. 5 (May 2014), pp. 403-415
DOI: 10.4169/amer.math.monthly.121.05.403
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Page Count: 13
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Rethinking Set Theory
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Abstract Mathematicians manipulate sets with confidence almost every day, rarely making mistakes. Few of us, however, could accurately quote what are often referred to as 'the' axioms of set theory. This suggests that we all carry around with us, perhaps subconsciously, a reliable body of operating principles for manipulating sets. What if we were to take some of those principles and adopt them as our axioms instead? The message of this article is that this can be done, in a simple, practical way (due to Lawvere). The resulting axioms are ten thoroughly mundane statements about sets.

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