# Oberseminar Mathematische Logik Wintersemester 2012/2013

 Mathematisches Institut Abteilung für Math. Logik

Dies ist die Homepage des Oberseminars "Mathematische Logik" im Wintersemester 2012/2013.

### Zeit und Ort

Mi 16:30-18:00, SR 404 in der Eckerstr. 1, vorher ab kurz nach 4 Tee in Zimmer 310

### Vorträge

• 24.10.2012
16 Uhr, Habilitationskolloquium Emanuel Scheidegger
Kein Oberseminar

• 31.10.2012
Heike Mildenberger
Combinatorics with block sequences
Abstract: I will talk on a forcing construction of a model in which every non-meagre filter is ultra by finite-to-one and at the same time the semifilter trichotomy does not hold. This trichotomy says: Every semifilter is either meagre or comeagre or ultra by finite-to-one. A semifilter is a subset of [omega]^\omega that is closed under almost supersets.

• 7.11.2012
Martin Ziegler
Indicernibles
Abstract: We give a simple proof of Shelah's theorem on the existence of tree indiscernibles.
• 14.11.2012
Heike in Toronto
• 21.11.2012
Arno Pauly
Beyond effective descriptive set theory
Abstract: While effective descriptive set theory has widely succeeded in providing effective counterparts to results from descriptive set theory pertaining to the projective hierarchy, some results from the lower levels of the Borel hierarchy such as the Jayne Rogers theorem resisted effectivization. Based on the notion of non-deterministic Type-2 computation, a proof of a computable Jayne Rogers theorem is given. For this, a more uniform approach to descriptive set theory in line with computable analysis is crucial - and distinct from the usual notions in descriptive set theory. As a further step, it is demonstrated how the Banach Hausdorff Lebesgue theorem linking Baire class n to Sigma-n+1 measurability follows as a corollary of a simple observation about endofunctors on the category of represented spaces. Together, this results are used to argue that represented spaces provide a very natural setting for descriptive set theory.
• 28.11.2012
Giorgio Laguzzi
Silver measurabilty without Miller measurability
Abstract: In the 1980s, Shelah invented a deep and rather mysterious construction to build strongly homogeneous algebra, called amalgamation. Together with the notion of sweet forcing, it was the amazing technique to get a model where all sets have the Baire property, without using inaccessible cardinals. The aim of the talk is to present an (absolutely less ambitious) application of Shelah´s amalgamation to obtain a model where all sets are Silver measurable but there exists a non-Miller measurable set.
• 5.12.2012
Luca Motto Ros
Wadge-like reducibilities on arbitrary (quasi-)Polish spaces
• 12.12.2012
Heike in Paris

• 19.12.2012
Jeff Serbus
Cardinal Invariants and the P-Ideal Dichotomy
• 9.1.2013
Philipp Schlicht
Title: Perfect subsets of generalized Baire spaces and Banach-Mazur games
Abstract: Let $\kappa$ be an uncountable cardinal with $\kappa^{< \kappa} = \kappa$. We consider the generalized Baire space of functions $f : \kappa \to \kappa$ with basic open sets $U_s = \{f \in \kappa^\kappa \mid s \subseteq f \}$ for $s \in {}^{< \kappa} \kappa$. A subset of $\kappa^\kappa$ is perfect if it is the set of branches of a $< \kappa$-closed subtree of ${}^{< \kappa} \kappa$ which splits above every node. We prove that after an inaccessible $\lambda > \kappa$ is collapsed to $\kappa^+$, every set $A \subseteq \kappa^\kappa$ definable from ordinals and subsets of $\kappa$ either has size $\leq \kappa$ or a perfect subset, and that the Banach-Mazur game for $A$ is determined.
• 16.1.2013
Juan-Diego Caycedo
Title: The Pila-Zannier proof of the Manin-Mumford conjecture
• 23.1.2013
Giorgio Laguzzi
Title: Amoeba of Sacks forcing without Cohen reals
• 29.1.2013 ausnahmsweise Dienstag von 11:30 bis 13 Uhr, SR 318
Alexander Prestel
Title: On rings of continuous p-adic valued functions
Last update on Jan. 21, 2013, H.M.