Place: Fields Institute (Room 210)
Date: May 27th, 2016 (13:30-15:00)
Speaker: Fulgencio Lopez
Title: Banach spaces from Construction Schemes
Abstract: In 2011 J. Lopez-Abad and S. Todorcevic used forcing to construct a
Banach space with an $\varepsilon$-biorthogonal system that didn’t have $\delta$-biorthogonal systems for every $1\leq\delta<\varepsilon$. We show that there is a Banach space with the same property provided there is a capturing Construction Scheme.
Set theory workshop
The workshop will be held at the University of Illinois at Chicago on October 20-23. Topic will cover forcing, large cardinals, applications of set theory. We will have three tutorials from leading experts and several talks by younger researchers.
The invited speakers are:
Travel support is available. Requests for such should be directed to Dima Sinapova at email@example.com. Such requests will be handled on a case-by-case basis within the limits of the budget. Graduate students, young researchers, female mathematicians and members of underrepresented groups are particularly encouraged to apply.
Tuesday, May 31, 2016, 17:15
Wrocław University of Technology, 215 D-1
Speaker: Wiesław Kubiś (Czech Academy of Sciences, KSW University)
Title: Abstract Banach-Mazur game
We will discuss an infinite game in which two players alternately choose some objects (structures) from a given class. The only rule is that at each move the structure chosen by the player should extend the one chosen in the previous move by the opponent. One of the players wins if the limit of the chain of structures resulting from the play is isomorphic to some concrete (fixed in advance) object. We will show some basic results and relevant examples concerning the existence of winning strategies.
BGU Seminar in Logic, Set Theory and Topology.
Time: Tuesday, May 24th, 12:30-13:45.
Place: Seminar room -101, Math building 58.
Title: Custom-made Souslin trees
We propose a parameterized proxy principle from which $\kappa$-Souslin trees with various additional features can be constructed, regardless of the identity of $\kappa$. We then introduce the *microscopic approach*, which is a simple method for deriving trees from instances of the proxy principle. As a demonstration, we give a construction of a coherent $\kappa$-Souslin tree that applies also for $\kappa$ inaccessible.
Place: Fields Institute (Room 210)
Date: May 20, 2016 (13:30-15:00)
Speaker: Asger Tornquist
Title: An invariant set-theoretic approach to Mathias’ theorem
Abstract: Mathias proved in 1969 that there are no infinite analytic
maximal almost disjoint families of subsets of $\omega$. His proof is
essentially Ramsey theoretical. A few years ago I found a “classical” proof
of this theorem which uses a tree/derivative argument. But in this talk, I
will give yet another proof, this time one that is closer in spirit to
Mathias’ original proof, but which avoids the Ramsey theoretical machinery
by instead using a bit of garden-variety invariant descriptive set theory.
Place: Fields Institute (Room 210)
Date: May 13, 2016 (13:30-15:00)
Speaker: Peter Koellner
Title: Large Cardinals Beyond Choice
The hierarchy of large cardinals provides us with a canonical means to
climb the hierarchy of consistency strength. There have been many
purported inconsistency proofs of various large cardinal axioms. For
example, there have been many proofs purporting to show that
measurable cardinals are inconsistent. But to date the only proofs
that have stood the test of time are those which are rather
transparent and simple, the most notable example being Kunen’s proof
showing that Reinhardt cardinals are inconsistent. The Kunen result,
however, makes use of AC, and long standing open problem is whether
Reinhardt cardinals are consistent in the context of ZF.
In this talk I will survey the simple inconsistency proofs and then
raise the question of whether perhaps the large cardinal hierarchy
outstrips AC, passing through Reinhardt cardinals and reaching far
beyond. There are two main motivations for this investigation. First,
it is of interest in its own right to determine whether the hierarchy
of consistency strength outstrips AC. Perhaps there is an entire
“choiceless” large cardinal hierarchy, one which reaches new
consistency strengths and has fruitful applications. Second, since the
task of proving an inconsistency result becomes easier as one
strengthens the hypothesis, in the search for a deep inconsistency it
is reasonable to start with outlandishly strong large cardinal
assumptions and then work ones way down. This will lead to the
formulation of large cardinal axioms (in the context of ZF) that start
at the level of a Reinhardt cardinal and pass upward through Berkeley
cardinals (due to Woodin) and far beyond. Bagaria, Woodin, and I
have been charting out this new hierarchy. I will discuss what we have
found so far.
A graduate summer school in set theory will be held July 25 – August 5 2016 at the University of California Irvine.
The subject of the summer school will be singular cardinal combinatorics, with a focus on PCF theory. The school will begin with a thorough treatment of PCF and related topics in combinatorial set theory, including club guessing and approachability. After this the school will treat interactions between PCF and other areas of set theory (including for example large cardinals, forcing axioms, reflection principles and squares).
The instructors will include James Cummings (CMU) and Christopher Lambie-Hanson (Hebrew University of Jerusalem). Lectures will be held Monday-Friday in each of the weeks July 25-29 and August 1-5. Each day will include two 90-minute lectures and two 90-minute discussion periods.
Participants will be housed in student housing on the Irvine campus. The school will fully support US citizens and permanent residents: this includes housing, meals, and travel costs (from US cities using US carriers).
If you are a graduate student and are interested in attending the summer school, please write to firstname.lastname@example.org with a short statement about your background in set theory and your interest in attending.
The web page for the summer school is
This summer school is supported by the National Science Foundation grant DMS-1044150 as part of the program EMSW21-RTG: Logic in Southern California.
Camilo Enrique Argoty from the Sergio Arboleda University in Bogota, Colombia visits Institute for Research in Fundamental Sciences in Tehran, Iran between May 4 and May 12, 2016 for giving some lectures on the model theory of Hilbert spaces. This mini course gives a panorama of model theory of Hilbert spaces in two frameworks: continuous first order logic and abstract elementary classes. The program of the sessions is as follows:
First session: Basic Hilbert space Model Theoretic Properties: Categoricity, stability, characterization of types, quantifier elimination, characterization of non-forking
Second session: Hilbert spaces with a normal operator: Elementary equivalence, $\aleph_0$ categoricity up to perturbations, types as spectral measures, quantifier elimination, non-forking, orthogonality and domination.
Hilbert spaces with a closed unbounded self-
adjoint operator: Metric abstract elementary classes (MAEC’s); a
for a Hilbert space with a closed unbounded self-adjoint operator; continuous first order elementary equivalence; types as spectral measures; non-forking, orthogonality and domination.
Fourth session: Model theory of representations of C*-algebras: Elementary equivalence; $\aleph_0$ categoricity up to perturbations; the generic representation of a C*-algebra; homoeomorphism of the stone space and quasi-state space and quantifier elimination; Non-forking, orthogonality and domination.
Fifth session: Further work: Elementary equivalence in *-representations of *-algebras