Blockfilters as Parameter Sets of Tree-Forcings
Dienstag, 21.6.22, 14:30-15:30, Raum 404, Ernst-Zermelo-Str. 1
The space of blocks consists of all non-empty finite sets of natural numbers. Given any filter on the natural numbers, the sets of blocks of filter elements generate a filter on the blockspace and, vice versa, each filter on the blockspace yields a filter on the natural numbers by taking unions of filter elements.\nIn this talk, we will make some observations about this relation and the question of whether the maximality of filters is or can possibly be preserved by it. As an application we will show how filters and coideals on the blockspace can be used as parameter sets of tree-forcings with the aim of diagonalizing a given filter on the natural numbers.\n \n
Generalised Tree Properties
Dienstag, 28.6.22, 14:30-15:30, Raum 404, Ernst-Zermelo-Str. 1
The talk will be a survey of my master's thesis. The topic of the thesis are two cardinal properties which are similar to the tree property and arise naturally from the consideration of a generalised tree.\nWe will first introduce both properties and then outline their similarities and differences, both in the way they can be proven consistent at small cardinals and what they imply.\nWe will show that, despite being equivalent for inaccessible cardinals, one property is strictly stronger than the other at small cardinals.