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UID:20260903T041007EDT-5812e5iaoM@132.216.98.100
DTSTAMP:20260903T081007Z
DESCRIPTION:The treatment of Cantorian sets by Bourbakian abstract set-theo
 ry\n\nAbstract sets\, that is\, sets with 'ur-elements'\, elements with no
  individuality other than being members of the set in question\, have been
  around from the start\, for Dedekind\, Cantor\, and others. They became o
 f importance for Bourbaki\, who insists that the identity of a mathematica
 l object lies in its structural relations to other objects\, rather than i
 n an intrinsic identity. Lawvere's first-order theory of the category of s
 ets (FOTCS) and his subsequent topos theory are decisive steps towards a s
 et-theory that allows only abstract sets. I have introduced a simple forma
 l system of abstract set-theory based on dependent types for which Bourbak
 i's requirement 'all properties must be invariant under isomorphisms' hold
 s true as a meta-theorem in the strong ('parametric') form demanded by Bou
 rbaki (in Lawvere's FOTCS\, as Colin McLarty has shown\, the weaker non-pa
 rametric version is true only). This time I want to emphasize the inclusiv
 eness of the new abstract set-theory\, not shared by topos theory in a suf
 ficiently natural way\, by explaining that\, in abstract set theory\, pres
 ent-day epsilontic Cantorian set-theory can be formulated as a theory of a
  particular Bourbakian 'species of structures'.\n
DTSTART:20181206T190000Z
DTEND:20181206T210000Z
LOCATION:Room 422\, CA\, Département de philosophie\, 2910 Edouard-Montpeti
 t
SUMMARY:Michael Makkai\, McGill University
URL:https://www.mcgill.ca/mathstat/channels/event/michael-makkai-mcgill-uni
 versity-292215
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