KGRC Research Seminar – 2017‑04‑26 at 4pm
Speaker: Matteo Viale (Università di Torino, Italy)
Abstract: ￼I overview several aspects of forcing axioms which (in my eyes) give solid mathematical arguments explaining why these axioms are so useful in establishing new (consistency) results and/or theorems.
- The first aspect outlines that forcing axioms are natural strengthenings not only of Baire’s category theorem, but also of the axiom of choice (these are two of the most useful non-constructive principles in mathematics), and also strengthenings of most large cardinal axioms (at least for cofinally many of them).
- The second aspect outlines that Shoenfield’s absoluteness, Cohen’s forcing theorem, and Los theorem for standard ultrapowers of a first order structure by a non principal ultrafilter are all specific instances of a more general form of Los theorem which can be declined for what I call boolean ultrapowers.
- The third aspect outlines how strong forcing axioms and Woodin’s generic absoluteness results are two sides of the same coin and will try to explain how stronger and stronger forms of generic absoluteness can be obtained by asserting stronger and stronger forcing axioms. In this context category theoretic ideas start to play a role and we are led to analyze forcings whose conditions are (certain classes of) forcing notions and whose order relation is given by (certain classes of) complete embeddings.
There is a surprising analogy between the theory of these class forcings, the theory of towers of normal ideals, and many of the classical arguments yielding generic absoluteness results. For what concerns the first two aspects of my talk, I do not claim authorship of essentially none of the result I will be talking about, nonetheless it is hard to attribute correctly the relevant results.
Tuesday, April 25, 2017, 17:15
Wrocław University of Technology, 215 D-1
Speaker: Marcin Michalski (Wroclaw University of Science and Technology)
Title: Luzin’s theorem
In 1934 Nicolai Luzin proved that each subset of the real line can be decomposed into two full subsets with respect to ideal of measure or category. We shall present the proof of this result partially decoding his work and we will also briefly discuss possible generalizations.
This is an announcement for an NSF-funded conference on “Applications
of Model Theory to Operator Algebras” to be held at the University of
Houston from July 31 — August 4, 2017. This conference will feature a
lecture series by our main speaker, Ilijas Farah, as well as several
plenary research talks by various experts in Operator Algebras and
The purpose of this conference is two-fold: First, to serve as a
“master class” for non-experts and young researchers to learn about
fundamental concepts presented by Professor Ilijas Farah, a leading
expert and renowned expositor of these topics; and second, to inform
and update experts in other areas of operator algebras about the
latest advances and achievements of the subject. More information on
these talks, and the topics covered, can be found on the conference
We hope you will be able to attend.
Mehrdad Kalantar (University of Houston)
Mark Tomforde (University of Houston)
Ping Wong Ng (University of Louisiana at Lafayette)
Leonel Robert (University of Louisiana at Lafayette)
University of Notre Dame, Logic Seminar • 125 Hayes-Healy Hall
Tue May 2, 2017 2:00PM – 3:00PM
Speaker: Andres Caicedo – Mathematical Reviews
Title: Real-valued measurability and Lebesgue measurable sets
Abstract: I will show that the existence of atomlessly measurable cardinals does not settle the range of Lebesgue measure on the projective sets.
A 2-week summer school will take place at UC Irvine from Aug. 14 – 25, 2017. The topic of the school will be classification problems in ergodic theory. Lectures will be given by Peter Burton
, Matt Foreman
, and Brandon Seward
- The first week will treat positive classification results and associated tools. We will primarily focus on entropy theory, starting with the classical entropy theory for actions of countable amenable groups and ending with the quite recent developments of entropy theory for actions of countable non-amenable groups (in particular sofic groups).
- The second week will be concerned with anti-classification results: results showing that classifications are not possible with countable resources. We begin with a review of naive descriptive set theory and then discuss classification in this framework. We proceed to show that the classification problem is not solvable for Z-actions, even of real analytic diffeomorphisms of the torus. Finally, we place the classification problems in the hierarchy of analytic equivalence relations under Borel reducibility.
The deadline for applications is May 15, however late applications will still be considered on a case-by-case basis. Funding is available for US citizens and permanent residents (per grant restrictions). More information can be found here:
SGSLPS 2017 Spring meeting on “Borel Reducibility of Equivalence Relations”
Université de Lausanne (Unil), Amphipôle, Room 340
29 May 2017, 10:30 – 17:00
The SGSLPS 2017 Spring meeting on “Borel Reducibility of Equivalence Relations” will feature four hour-long talks by leading experts in the field. The first talk will be introductory and will aim at a general audience.
- Andrew Brooke-Taylor (University of Leeds, Leeds)
- Raphaël Carroy (Kurt Gödel Research Centre, Vienna)
- Julien Melleray (Université Claude Bernard Lyon 1, Lyon)
- Luca Motto Ros (Università di Torino, Turin
About the subject:
Classification has always been a central theme in mathematics. The study of Borel Reducibility of Equivalence Relations deals with the classification of points of standard Borel spaces up to equivalence relations by explicit, or Borel, mappings between such spaces.
This idea gives rise to a notion of complexity of equivalence relations, and tools from Descriptive Set Theory are used to compare such relations and measure their complexities.
The SGSLPS 2017 Spring meeting is organised by the Swiss Graduate Society for Logic and Philosophy of Science, SGSLPS
, with funding by the Swiss Academy of Sciences
The Swiss Graduate Society for Logic and Philosophy of Science (SGSLPS) is an association of advanced undergraduate and graduate students with a distinctive interest in the large domains of logic and philosophy of science
For more information, visit: http://sgslps.ch/upcoming