Quotients of Boolean algebras and regular subalgebras (Q964454)

The main theorem is that in any generic extension of \(M\) containing a new real there is an almost disjoint refinement of \([\omega]^\omega\) (in the \(M\) sense). This is applied to \({\mathcal P}(\omega)\)/fin to obtain information about the cardinal functions \(\mathfrak b\) and \(\mathfrak h\), using the notion of a splitting real. The minimal ideal \(I\) such that there is a regular embedding of \({\mathcal P}(\omega)\)/fin (in the sense of \(M\)) into \(({\mathcal P}(\omega)/\text{fin})/I\) (in the sense of \(M[G]\)) is investigated.