Giorgio Laguzzi :
Tree-Forcing Notions
Time and place
Thursday, 24.10.19, 17:00-18:00, Hörsaal II, Albertstr. 23b
Abstract
During the 1960s Cohen and Solovay introduced and developed the method of\nforcing, which soon became a key technique for building various models of\nset theory. In particular such a method was crucial for answering questions\nconcerning the use of the axiom of choice to construct non-regular objects\n(such as non-Lebesgue measurable sets, non-Baire sets, ultrafilters) and to\nanalyse possible sizes of several types of subsets of reals (such as\ndominating and unbounded families, and other so-called cardinal\ncharacteristics).\nOne of the key ideas in both cases is the notion of a tree-forcing, i.e.\na partial order consisting of a specific kind of perfect trees. In this\ntalk, after a brief historical background, we will focus on some results\non Silver, Miller and Mathias trees. We will also see applications of\ninfinitary combinatorics and tree-forcing in the context of\ngeneralized descriptive set theory and the study of social welfare\nrelations\non infinite utility streams.\n