... cardinals are those ordinals κ such that no earlier ordinal has the same car-dinality as κ. The finite cardinals are 0, 1, 2, ;andωis the smallest in nitecardinal;(iii) the cardinality of a set A, ... written |A| , is that (unique) cardinal κ such that A andκ have the same cardinality;(iv) |A| ·|B|= |A B|[= max( |A| , |B|) if either is in nite and A, B = ∅] .A B=∅⇒ |A| +|B|= |A B| [= max( |A| , |B|) ... operations ∨ and ∧ by a ∨ b =sup {a, b}, and a ∧ b =inf {a, b}.Suppose that L is a lattice by the first definition and ≤ is defined as in (A) . From a a = a follows a ≤ a. If a ≤ b and b ≤ a then a...