Rethinking Set Theory
2014; Taylor & Francis; Volume: 121; Issue: 5 Linguagem: Inglês
10.4169/amer.math.monthly.121.05.403
ISSN1930-0972
Autores Tópico(s)History and Theory of Mathematics
ResumoAbstractAbstractMathematicians 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. This article is part of the following collections: Chauvenet Prize: 2000s, 2010s, and 2020s Additional informationNotes on contributorsTom LeinsterTOM LEINSTER studied at Oxford and Cambridge, and held positions at Cambridge, the Institut des Hautes Études Scientifiques, and the University of Glasgow before taking up his current job in Edinburgh. He is interested in category theory and its applications, especially some of the more unusual ones. He is a professionally qualified masseur.
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