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

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Constructivist and Structuralist Foundations: Bishop’s and Lawvere’s Theories of Sets (2009)

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by Erik Palmgren

Citations:

7 - 1 self

BibTeX

@MISC{Palmgren09constructivistand,
    author = {Erik Palmgren},
    title = {Constructivist and Structuralist Foundations: Bishop’s and Lawvere’s Theories of Sets},
    year = {2009}
}

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Abstract

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-Löf. The theory, CETCS, provides a structuralist foundation for constructive mathematics in the style of Bishop.

Keyphrases

structuralist foundation lawvere theory lawvere elementary theory predicative version informal set theory constructive type theory standard model constructive mathematics

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