# Amalgamation of two ccc algebras may collapse the continuum

The claim that appears in the title of this question is mentioned in the paper "On Shelah's amalgamation" by Judah and Roslanowski. I'd really like to see a proof of this fact, but unfortunately I couldn't find any reference for this claim.

So my question is: Are there relatively simple examples of amalgamation of ccc algebras that collapse the continuum? If there aren't any simple examples, then a reference for a harder example would be welcome as well.

-

Suppose CH holds and there is a Souslin tree $T$. (For example, suppose $V=L$.) Then $T$ itself can be regarded as a forcing notion; it has ccc and it adjoins a generic path through $T$. There is also a ccc forcing notion that specializes $T$; a condition here is a finite partial function from $T$ into $\omega$ such that any two comparable nodes in the domain of the condition are assigned distinct values; the union of the generic filter is a function from all of $T$ into $\omega$ that never takes the same value at two comparable nodes of $T$. If you force with both of these, then the specializing function restricted to the generic path gives a one-to-one map of $\omega_1$ into $\omega$. So you've collapsed $\aleph_1$; since I assumed CH, this means you've collapsed the cardinal of the continuum.