In this thesis the author gives a logically precise description of how one can apply the theory of Von Neumann algebras to embeddable \(AW^*\)- algebras, that is, a transfer principle from Von Neumann algebras in Boolean-valued set theory to embeddable \(AW^*\)-algebras. This is the main theorem in this note.
One of the applications of the main theorem is that every embeddable \(AW^*\)-algebra is centrally embeddable. And the author proved that every \(AW^*\)-algebra admits a unique direct sum decomposition into an embeddable algebra and one which is non-embeddable. This fact shows that the crucial pathologies of \(AW^*\)-algebras come from non-embeddable \(AW^*\)-algebras since the embeddable part is clear from the transfer principle.
The author also gives a special characterization for an embeddable \(AW^*\)-algebra with centre using the transfer principle.