Bohuslav Balcar, Michal Doucha, Michael Hrušák
Published 2012-11-14, updated 2013-03-03Version 3
Building on previous work of [BPS] 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 $\mathfrak c$ 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.
Henkin constructions of models with size continuum
Strongly meager sets of size continuum
On $\mathbb R$-embeddability of almost disjoint families and Akemann-Doner C*-algebras
![QR code for arXiv:1211.3350 [math.LO]](http://oss.arxitics.com/images/favicon.svg)