Dies ist die Homepage des Oberseminars "Mathematische Logik" im
Wintersemester 2014/15.
Prof. Mildenberger.
Prof. Ziegler hat ein Forschungssemester.
Zeit und Ort
Mi 16:3018:00, SR 404 in der Eckerstr. 1, vorher
ab kurz nach 4 Tee in Zimmer 310
Vorträge

October, 22
Giorgio Laguzzi Between Sacks and random for inaccessible kappa
Abstract: A nontrivial issue concerning treelike forcings in the generalized
framework is to introduce a randomlike forcing, where randomlike means to be
κκbounding, < κclosed and κ+cc simultaneously. Shelah managed to do that for
κ weakly compact. In this talk we aim at introducing a forcing satisfying these
three properties for κ inaccessible, and not necessarily weakly compact.
This is joint work with Sy Friedman.

October, 29
Heike Mildenberger Reflection principles
This is an introduction to reflection principles, on how to force
them and on their consistency strength. This is based on work by Justin Moore
and Stevo Todorcevic.

November, 5
Christoph Bier Basic Notions: Forcing

November, 12
David Chodounsky Yc.c. and Yproper forcings
I will introduce a new type of properties of c.c.c. and proper forcing notions, of which the
Yc.c. and Yproper are the two most prominent examples. The Yc.c. is an intermediate property
between σcentered and c.c.c., and Yproper is intermediate between strongly proper and proper.
These properties have interesting consequences and behave nicely with respect forcing
iterations.

November, 19
Philipp Lücke
Representing sets of cofinal branches as continuous images
Let $\kappa$ be an infinite cardinal and $T$ be a tree of height $\kappa$. We equip the set $[T]$ of all branches of length $\kappa$ through $T$ with the topology whose basic open subsets are sets of all branches containing a given node in $T$. Given a cardinal $\nu$, we consider the question whether $[T]$ is equal to a continuous image of the tree of all functions $s:\alpha\longrightarrow\nu$ with $\alpha<\kappa$. This is joint work with Philipp Schlicht.

November, 26
Ilya Sharankou
Overview of the generalized combinatorial cardinal characteristics
I will talk about how the combinatorial cardinal characteristics
reviewed in [Blass, Combinatorial Cardinal Characteristics of the
Continuum] can be generalized to uncountable cardinals kappa and what is
known about consistency results for them.

December, 3
Otmar Spinas
Silver trees and Cohen reals
I will sketch the main ideas of my recent result that the
meager ideal is Tukey reducible to the Mycielski ideal. The latter one is
the ideal associated with Silver forcing. This implies that every
reasonable amoeba forcing for Silver adds a Cohen real. This has been open
for some years.

December, 10
Lothar Krapp
Schanuel's Conjecture and Exponential Fields
Schanuel's Conjecture states that for a collection of n complex
numbers z_1, ..., z_n, linearly independent over the field of
rational numbers, the transcendence degree of z_1, ..., z_n,
exp(z_1), ..., exp(z_n) is at least n.
Zilber constructs in [Zilber, Pseudoexponentiation on
algebraically closed fields of characteristic zero] a sentence
whose models are structures called strongly
exponentiallyalgebraically closed fields with
pseudoexponentiation, which are unique in every uncountable
cardinality. One of their main properties is that Schanuel's
Conjecture holds in those fields.
Firstly, I will outline the properties of Zilber's fields.
Secondly, I will sketch the proof given in [Marker,
A Remark on Zilber's Pseudoexponentiation] showing that, if one
assumes Schanuel's Conjecture, the simplest case of one of the
axioms of Zilber's fields holds in the complex exponential field.

December, 17
Giorgio Laguzzi Amoeba and tree ideals
I will talk about what I asked to Spinas in the end of his talk, i.e., whether an
amoeba for Silver might add Cohen reals. Two weeks ago he proved that add(J(Silver)) is at most
add(M). However this is not strictly sufficient to infer that any proper amoeba for Silver does
add Cohen reals, but only that it does not have the Laver property. I will clarify this
issue. If there will be any time left I will also present some results about other tree ideals,
which are part of a joint work, still in preparation, with Yurii Khomskii and Wolfgang
Wohofsky.

January, 7, 2015
Kein Oberseminar. Hausbegehung und Sitzungen im Rahmen des Akkreditierungsverfahrens.

January, 14, 2015
Andrew BrookeTaylor
Cardinal characteristics at supercompact kappa in the small u(kappa), large 2^kappa model
When generalising arguments about cardinal characteristics of the continuum to cardinals kappa greater than
omega, one frequently comes up against the problem of how to ensure that a filter built up through an iterated
forcing remains kappa complete at limit stages of small cofinality. A technique of Dzamonja and Shelah is
useful for overcoming this problem; in particular, there is a natural application of this technique to obtain
a model in which 2^kappa is large but the ultrafilter number u(kappa) is kappa^+. After introducing this
model, I will talk about joint work with Vera Fischer (Technical University of Vienna) and Diana Montoya
(University of Vienna) calculating many other cardinal characteristics at kappa in the model and its variants.

January, 21, 2015
JuanDiego Caycedo
On the theory of universal specializations of Zariski structures
I will report on ongoing joint work with Alex Berenstein and Alf Onshuus on proving that all universal
specializations of models of the theory of a fixed Zariski structure share the same complete theory and
finding axioms for this theory. I will show this in the most fundamental particular cases (sets, vector
spaces, algebraically closed fields) and discuss our progress in the general case.
I spoke about this topic once before in the seminar and the current talk is a continuation of the previous
one, but no knowledge of the content of that talk will be assumed.

January, 28, 2015
kein Oberseminar

February, 4, 2015
Moritz Müller
Partially definable forcing and weak arithmetics
Given a nonstandard model M of arithmetic we want to expand it
by interpreting a binary relation symbol R such that R^M does something
prohibitive, e.g. violates the pigeonhole principle in the sense that R^M
is a bijection from n+1 onto n for some (nonstandard) n in M. The goal is
to do so saving as much as possible from ordinary arithmetic. More
precisely, we want the expansion to satisfy the least number principle for
a class of formulas as large as possible. We describe a forcing method to
produce such expansions and revisit the most important results in the
area.

February, 11, 2015
Heike Mildenberger
A new forcing order
We will see a new type of expanded Sacks forcing with
many combinatorial properties.
