Complete embeddings of the Cohen algebra into three families of c.c.c., non-measurable Boolean algebras

The Cohen algebra embeds as a complete subalgebra into three classic families of complete, atomless, c.c.c., non-measur-able Boolean algebras; namely, the families of Argyros al-gebras and Galvin-Hajnal algebras, and the atomless part of each Gaifman algebra. It immediately follows that the weak (ω, ω)-distributive law fails everywhere in each of these Boolean algebras. 1. Introduction. Von Neumann conjectured that the countable chain condition and the weak (ω, ω)-distributive law characterize measurable algebras among Boolean σ-algebras [Mau]. Consistent counter-examples have been obtained by Ma-haram [Mah], Jensen [J], Glówczyński [Gl], and Veličkovic ́ [V]. However