Type: Article

Base tree property

Bohuslav, Balcar; Doucha, Michal; Hrusak, Michael;

Abstract:

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