Algumas aplicações de p-pontos

Abstract

In this work we analyze the concept of \(p\)-points in \(\omega\) and its relation with forcing, in particular Sacks forcing and side-by-side Sacks forcing. With this we verify that the existence of \(p\)-points with character \(\aleph_1\) is consistent with arbitrarily large \(2^{\aleph_0}\). We then analyze two applications involving \(p\)-points: the construction of a graph without unfriendly partitions and the analysis of the homogeneity of the space \(\beta\omega \setminus \omega\).