4 research outputs found
A convergence on Boolean algebras generalizing the convergence on the Aleksandrov cube
We compare the forcing related properties of a complete Boolean algebra B
with the properties of the convergences (the algebraic convergence)
and on B generalizing the convergence on the Cantor and
Aleksandrov cube respectively. In particular we show that is a
topological convergence iff forcing by B does not produce new reals and that
is weakly topological if B satisfies condition
(implied by the -cc). On the other hand, if is a
weakly topological convergence, then B is a -cc algebra or in
some generic extension the distributivity number of the ground model is greater
than or equal to the tower number of the extension. So, the statement "The
convergence on the collapsing algebra B=\ro
((\omega_2)^{<\omega}) is weakly topological" is independent of ZFC