Base tree property (Q2264116)

A partially ordered set is called \(\sigma\)-closed if every countable decreasing sequence of its elements has a lower bound. In this paper: 1) It is shown that every partially ordered set with a dense \(\sigma\)-closed subset of size continuum has a base tree; 2) The \(\sigma\)-closed forcings of size continuum as the regular subalgebras of a collapsing algebra are characterized.