# Class

[[category:There are several definitions of a class in use. The following definition is given by Copi. ^{[1]}
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,

- a ∩ ~a = 0
- a ∪ ~a = 1

5. and for every a, b, and c in C,

- a ∪ (b ∩ c) = (a ∪ b) ∩ (a ∪ c)
- a ∪ (b ∩ c) = (a ∩ b) ∪ (a ∩ c).

## ReferencesEdit

- ↑ Symbolic Logic. Fifth edition. Pages 175-176.