User talk:Lord Farin/Sandbox/Definition:Boolean Algebra

Lattices
I think Boolean algebras are often defined as bounded distributive lattices with certain additional properties. I think it'd probably be valuable to add that, and then see how much of each of the other approaches is significantly different. --Dfeuer (talk) 15:55, 31 December 2012 (UTC)


 * Yes, it is in the pipeline to define a BA as "complemented distributive lattice". That's the main reason why I have refrained from pushing this to main. But to support that I'll have to rework most of the Lattice Theory compartment first. --Lord_Farin (talk) 15:59, 31 December 2012 (UTC)


 * Thanks for doing all this work. --Dfeuer (talk) 16:58, 31 December 2012 (UTC)

Complements
One of many things we need to be careful about is whether, in a given definition, we specify a complement operator or complement elements. When elements, we need to prove uniqueness. Within any given axiom set, if elements are sufficient, we should offer that option, I believe. There seem to be an awful lot of ways to axiomatize these bloody things. --Dfeuer (talk) 18:58, 21 January 2013 (UTC)


 * I know. Cf. User talk:Prime.mover. --Lord_Farin (talk) 19:02, 21 January 2013 (UTC)