Hitoshi Furusawa
Strict point axiom in Dedekind categories is really strict
(joint work with Yasuo Kawahara)

A 
Dedekind category (or a locally complete division allegory)
is a convenient algebraic framework to treat relations, fuzzy relations,
and L-fuzzy 
relations. Concepts of points and the point axiom are
introduced in Dedekind categories to connect abstract formulae with
set-theoretical intuition. 
Strict point axiom is a variant of the point
axiom. In this talk, we show that assuming strict point axiom restrict a
Dedekind category to be a 
framework just for ordinary relations though
it does not look like.