Class

There are several definitions of a class in use. The following definition is given by Copi. An ordered 4-tuple (C,(∩,∪),~,(1,0)) is called a class if it satisfies the following axioms. 1. (C, ∩, 1) is an abelian monoid 2. (C, ∪, 0) is an abelian monoid 3. 0 ≠ 1 4. for every a in C, 5. and for every a, b, and c in C,
 * a ∩ ~a = 0
 * a ∪ ~a = 1
 * a ∪ (b ∩ c) = (a ∪ b) ∩ (a ∪ c)
 * a ∪ (b ∩ c) = (a ∩ b) ∪ (a ∩ c).