Comparison of Boolean algebras (Q1101111)

The authors present a construction of superatomic interval Boolean algebras which yields the following result: If \(\kappa\) is an uncountable cardinal then there are \(2^{\kappa}\) isomorphism types of superatomic Boolean algebras of cardinality \(\kappa\). This contrasts with the countable case, where the superatomic algebras form a chain of order-type \(\omega_ 1\). The construction uses stationary sets.