I came across a statement in the David and Osvaldo’s paper “There are no P-points in Silver extension” that:
under GCH, it is a well-known fact that $\omega_1 < \kappa$ copies of the countable support product of Prikry Silver forcing is $\omega_2$-cc.
However, as I am not familiar with the concept of countable support product and Prikry Silver forcing, I was unable to prove this. What would be the approach to proving this claim?
As for Prikry Silver forcing, I have been reading Halbeisen's combinatorial set theory and for countable support product, I have been reading Kunen's Set theory.