Talk:Heyting algebra
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This definition looks identical to that of the concepf of Boolean algebra: a Boolean algebra is a complemented distributive lattice, provided one includes boundedness in the definition of lattice. What is the difference, if any, supposed to be? Michael Hardy 03:27, 9 Nov 2003 (UTC)
Unclear, certainly. Heyting algebras are not in general Boolean algebras. The point is that negation is defined as not x = 'x implies bottom', and this doesn't in general satisfy not not x = x. I think relatively complemented mis-states the definition, which is presumably meant to be that x implies y always exists , as a supremum.
Charles Matthews 08:31, 9 Nov 2003 (UTC)