There are several equivalent definitions for Class Algebra in the literature. One of them was given by the late Irving M. Copi.  An equivalent definition is given here. Let C be a Mathics/class. Let ∪ and ∩ be w:binary operations on C and let 0 and 1 be elements of C. Then
- (C, (∪,∩), ~, (0,1)) is_a class_algebra
- ((C, ∪, ~, 0), (C, ∩, ~, 1)) is_a Mathics/semiclass_algebra and ((C, ∩, ~, 1), (C, ∪, ~, 0)) is_a Mathics/semiclass_algebra.
- Irving M. Copi. Symbolic Logic. Fifth edition