Constructivist and Structuralist Foundations: Bishop's and Lawvere's Theories of Sets

Details Constructivist and Structuralist Foundations: Bishop's and Lawvere's Theories of Sets Constructivist and Structuralist Foundations: Bishop's and Lawvere's Theories of Sets

2012-01-30

arxiv.org/abs/1201.6272v1

Mathematics

Logic

28 pages

Scientific paper

Bishop's informal set theory is briefly discussed and compared to Lawvere's
Elementary Theory of the Category of Sets (ETCS). We then present a
constructive and predicative version of ETCS, whose standard model is based on
the constructive type theory of Martin-L\"of. The theory, CETCS, provides a
structuralist foundation for constructive mathematics in the style of Bishop.

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