Combinatorics with block sequences
Mittwoch, 31.10.12, 16:30-17:30, Raum 404, Eckerstr. 1
Combinatorics with block sequences
Mittwoch, 31.10.12, 16:30-17:30, Raum 404, Eckerstr. 1
Indiscernibles
Mittwoch, 7.11.12, 16:30-17:30, Raum 404, Eckerstr. 1
We give a simple proof of Shelah's theorem on the existence\nof tree indiscernibles.
Silver measurabilty without Miller measurability
Mittwoch, 28.11.12, 16:30-17:30, Raum 404, Eckerstr. 1
In the 1980s, Shelah invented a deep and rather mysterious \nconstruction to build strongly homogeneous algebra, called amalgamation. \nTogether with the notion of sweet forcing, it was the amazing technique to\nget \na model where all sets have the Baire property, without using inaccessible \ncardinals. The aim of the talk is to present an (absolutely less ambitious) \napplication of Shelah´s amalgamation to obtain a model where all sets are \nSilver measurable but there exists a non-Miller measurable set. \n
Wadge-like reducibilities on arbitrary (quasi-)Polish spaces
Mittwoch, 5.12.12, 16:30-17:30, Raum 404, Eckerstr. 1
Cardinal Invariants and the P-Ideal Dichotomy
Mittwoch, 19.12.12, 16:30-17:30, Raum 404, Eckerstr. 1
Perfect subsets of generalized Baire spaces and Banach-Mazur games
Mittwoch, 9.1.13, 16:30-17:30, Raum 404, Eckerstr. 1
Let \(\bkappa\) be an uncountable cardinal with \(\bkappa^{< \bkappa} = \bkappa\). We consider the generalized Baire space of functions \(f : \bkappa \bto \bkappa\) with basic open sets \(U_s = \b{f \bin \bkappa^\bkappa \bmid s \bsubseteq f \b}\) for \(s \bin {}^{< \bkappa} \bkappa\). A subset of \(\bkappa^\bkappa\) is perfect if it is the set of branches of a \(< \bkappa\)-closed subtree of \({}^{< \bkappa} \bkappa\) which splits above every node. We prove that after an inaccessible \(\blambda > \bkappa\) is collapsed to \(\bkappa^+\), every set \(A \bsubseteq \bkappa^\bkappa\) definable from ordinals and subsets of \(\bkappa\) either has size \(\bleq \bkappa\) or a perfect subset, and that the Banach-Mazur game for \(A\) is determined.
The Pila-Zannier proof of the Manin-Mumford conjecture
Mittwoch, 16.1.13, 16:30-17:30, Raum 404, Eckerstr. 1
Amoeba of Sacks forcing without Cohen reals
Mittwoch, 23.1.13, 16:30-17:30, Raum 404, Eckerstr. 1
On rings of continuous p-adic valued functions
Dienstag, 29.1.13, 11:30-12:30, Raum 318, Eckerstr. 1