## Logic Seminar 17 Oct 2018 17:00 hrs at NUS

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 17 October 2018, 17:00 hrs

Room: S17#04-05, Department of Mathematics, NUS

Speaker: Dilip Raghavan

Title: Order dimension

URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

Abstract: We will present some results on the order dimension of
various partial orders, focusing on partial orders which are locally countable.
This is joint work with Kojiro Higuchi, Steffen Lempp and Frank Stephan.

## Reflections on Set Theoretic Reflection, Sant Bernat, November 16-19, 2018

Reflections on Set Theoretic Reflection

16-19 November 2018

Sant Bernat, Montseny, Catalonia

Set Theory Conference

Organised in partnership with the Clay Mathematics Institute

Keynote Speakers

• Peter Koellner (Harvard)
• Paul Larson (Miami)
• Menachem Magidor (Jerusalem)
• Jouko Väänänen (Helsinki and Amsterdam)
• W. Hugh Woodin (Harvard)

Organisers

• David Asperó (UEA, Norwich)
• Carles Casacuberta (IMUB, Barcelona)
• Miguel Ángel Mota (ITAM, México)
• Konstantinos Tsaprounis (UAegean, Samos)

Venue and Accommodation

The event will take place at Hotel Sant Bernat, located in the Montseny natural park, in Catalonia.

Lodging rates are in Euros and include three hotel nights with three meals per day (from lunch on Friday 16 up to breakfast on Monday 19) plus tourist taxes.

• Double room for single use: 427 €
• Shared double room: 317 €
• Shared triple room: 295 €

There is the possibility of arriving earlier and/or departing later from the hotel. In such a case, the additional costs are as follows (room prices refer to one extra night, including breakfast):

• Double room for single use: 70 €
• Shared double room: 43 €
• Lunch on Monday: 26 €

Transportation

Both on Friday 16 (arrival) and on Monday 19 (departure), transportation between El Prat airport of Barcelona and the hotel, passing through downtown Barcelona, will be arranged by the organisers. The bus ride from the airport to the hotel can take around two hours.

Further information on location and transportation is given here, including a map, bus schedule, car ride directions, train and taxi options.

Registration

The registration fee amounts to 75 € and includes a welcome cocktail, coffee breaks, and a mushroom hunting snack on Saturday 17. Instructions for registration and payment will be sent to pre-registered participants. Please contact the organisers for pre-registration.

List of Participants

So far the following people have pre-registered for the conference.

Contact

You may contact the organisers either directly or via the e-mail address 2018bagaria60 AT gmail DOT com.

The organisers gratefully acknowledge support from the Clay Mathematics Institute, the Foundation Compositio Mathematica, and the Institute of Mathematics of the University of Barcelona.

## Anush Tserunyan: Hyperfinite subequivalence relations of treed equivalence relations

Mathematical logic seminar – Oct 16 2018
Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         Anush Tserunyan
Department of Mathematics
University of Illinois at Urbana-Champaign

Title:     Hyperfinite subequivalence relations of treed equivalence relations

Abstract:

A large part of measured group theory studies structural properties of countable groups that hold “on average”. This is made precise by studying the orbit equivalence relations induced by free Borel actions of these groups on probability spaces. In this vein, the cyclic (more generally, amenable) groups correspond to hyperfinite equivalence relations, and the free groups to the treeable ones. In joint work with R. Tucker-Drob, we give a detailed analysis of the structure of hyperfinite subequivalence relations of a treed equivalence relation, deriving some of analogues of structural properties of cyclic subgroups of a free group. In particular, just like any cyclic subgroup is contained in a unique maximal one, we show that any hyperfinite subequivalence relation is contained in a unique maximal one.

## Monroe Eskew – Rigid ideals

Talk held by Monroe Eskew (KGRC) at the KGRC seminar on 2018-10-18.

Abstract: Using ideas from Foreman-Magidor-Shelah, one can force from a Woodin cardinal to show it is consistent that the nonstationary ideal on $\omega_1$ is saturated while the quotient boolean algebra is rigid. The key is to apply Martin’s Axiom to the almost-disjoint coding forcing to see how it interacts with a generic elementary embedding. This strategy requires the continuum hypothesis to fail. Towards showing the consistency of rigid ideals with GCH, the speaker investigated other coding strategies: stationary coding (with Brent Cody), a rigid version of the Levy collapse, and ladder-system coding (in recent work with Paul Larson). We have some equiconsistencies about rigid ideals on $\omega_1$ and $\omega_2$, as well as some global possibilities from very large cardinals. Some natural questions remain about $\omega_1$  and successors of singulars.

## Winter School, Hejnice, Jan 26–Feb 2, 2019

The Winter School in Abstract Analysis, section Set Theory & Topology will take place between January 26th and February 2nd 2019 in Hejnice, Czech Republic.

Tutorial speakers for the Winter School 2018 are:

James Cummings
Miroslav Hušek
Wiesław Kubiś

The registration is now open. The conference fee is 350 EUR and covers all expenses including the bus from Prague to Hejnice and back.

Registration deadline — December 31st, 2018

www.winterschool.eu

We hope to see you in January,
David Chodounský, Jan Grebík, Jan Starý and Jonathan Verner

## David Chodounský – Silver forcing and P-points

Research seminar, Kurt Gödel Research Center – Thursday, October 11th

Abstract: I will give a full proof of a joint result with O. Guzman regarding a
technique for destroying P-ultrafilters with Silver forcing. Time
permitting, I will present several applications.

## Gerhard Jäger – From fixed points in weak set theories to some open problems

Research seminar, Kurt Gödel Research Center –  October 9th

Abstract: Least fixed points of monotone operators are well-studied objects in many
areas of mathematical logic. Typically, they are characterized as the
intersection of all sets closed under the respective operator or as the
result of its iteration from below.

In this talk I will start off from specific $\Sigma_1$ operators in a
Kripke-Platek environment and relate fixed point assertions to alternative
set existence principles. By doing that, we are also led to some
“largeness axioms” and to several open problems.

## Logic Colloquium 2019, Prague, August 11 – 16, 2019

European Summer Meeting of the Association for Symbolic Logic, Logic Colloquium ’19 will take place during August 11th–16th in Prague, Czech Republic.

### Program Committee

Lev Beklemishev (Moscow, chair), Andrew Arana (Paris), Agata Ciabattoni (Vienna), Russell Miller (New York), Martin Otto (Darmstadt), Pavel Pudlák (Prague), Stevo Todorčević (Toronto), Alex Wilkie (Manchester)

### Organizing Committee

David Chodounský (co-chair), Jonathan Verner (co-chair), Petr Cintula, Radek Honzík, Jan Hubička, Pavel Pudlák, Jan Starý, Neil Thapen

website

## Piotr Koszmider: Uncountable constructions from CH using generic filters

Seminar: Working group in applications of set theory, IMPAN

Thursday, 11.10. 2018, 10:15, room 105, IMPAN

Speaker: Piotr Koszmider (IMPAN)

Title: “Uncountable constructions from CH using generic filters”

Abstact. We will present some old CH constructions due to S. Shelah. As usual they use transfinie induction, diagonalization and enumeration of all relevant objects in the first uncountable type. However, the use of the Martin’s axiom type arguments makes them additionally powerful.

Visit our seminar page which may include some future talks at https://www.impan.pl/~set_theory/Seminar/

## Clinton Conley: Realizing abstract systems of congruence II

Mathematical logic seminar – Oct 9 2018
Time: 3:30pm – 4:30 pm

Room: Wean Hall 8220

Speaker: Clinton Conley
Department of Mathematical Sciences
CMU

Title: Realizing abstract systems of congruence II

Abstract:

An abstract system of congruence (ASC) is simply an equivalence relation
on the power set of a finite set F satisfying some nondegeneracy
conditions. Given such an ASC and an action of a group G on a set X, a
realization of the ASC is a partition of X into pieces indexed by F such
that whenever two subsets A, B are asc-equivalent, the corresponding
subsets XA and XB of X can be translated to one another in the action.
Familiar notions like paradoxical decompositions can be easily formalized
and refined by the ASC language. Wagon, upon isolating this notion,
characterized those ASCs which can be realized by rotations of the sphere.
He asks whether there is an analogous characterization for realizing ASCs
using partitions with the property of Baire. We provide such a
characterization. This is joint work with Andrew Marks and Spencer Unger.