Abstract
Building on previous work from Balcar et al., Fund. Math. 110, 11-24 (1980) we investigate sigma-closed partial orders of size continuum.
We provide both an internal and external characterization of such partial orders by showing that (1) every sigma-closed partial order of size continuum has a base tree and that (2) sigma-closed forcing notions of density oe" correspond exactly to regular suborders of the collapsing algebra Coll(omega (1), 2 (omega). We further study some naturally ocurring examples of such partial orders.