## Eric Martin: Logic Programming as Classical Inference

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 17 February 2016, 17:00 hrs

Room: S17#05-11, Department of Mathematics, NUS

Speaker: Eric Martin

Title: Logic Programming as Classical Inference

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

Abstract: See http://www.comp.nus.edu.sg/~fstephan/abs20160217.pdf

## Fulgencio Lopez: Trees and Gaps from construction schemes

Place: Fields Institute (Room 210)

Date: February 12 , 2016 (13:30-15:00)

Speaker: Fulgencio Lopez

Title: Trees and Gaps from construction schemes

Abstract: Using a quite general Construction Scheme we construct a Suslin tree and a T-gap (a stronger notion than destructible gap). Joint work with S. Todorcevic.

## James Cummings: Proper forcing, side conditions and Baumgartner’s problem

Mathematical logic seminar – February 9 2016
Time:     12:30 – 13:30Room:     Wean Hall 8220

Speaker:         James Cummings
Department of Mathematical Sciences
CMU

Title:     Proper forcing, side conditions and Baumgartner’s problem

Abstract:

I will discuss the method of “proper forcing”, some tricks for building proper forcing posets, and applications old and new. The talk should be accessible to anyone who knows the rudiments of forcing.

Note: If you are planning to attend Itay’ Neeman’s forthcoming Appalachian Set Theory workshop, this talk will fill in some of the background.

## Twelfth Symposium on General Topology

### and its Relations to Modern Analysis and Algebra

www.toposym.cz

Toposym 2016 will be held on July 25–29, 2016 in Prague, Czech Republic under the auspices of the Institute of Mathematics of the Academy of Sciences of the Czech Republic and the Faculty of Mathematics and Physics of the Charles University.

Registration for the Toposym is now open.

### Invited speakers

The following mathematicians have agreed to give an invited talk.

• Alexander Arhangel’skii (Ohio University, USA & University of Moscow, Russia)
• Leandro Aurichi (Departamento de Matemática, Universidade de São Paulo, Brasil)
• Dikran Dikranjan (University of Udine, Italy)
• Alan Dow (University of North Carolina at Charlotte, USA)
• Michael Hrušák (National Autonomous University of Mexico)
• Ondrej Kalenda (Charles University in Prague, Czech Republic)
• Alexander Kechris (California Institute of Technology, USA)
• Piotr Koszmider (Mathematical Institute of the Polish of Academy of Sciences)
• Mikolaj Krupski (University of Warsaw, Poland)
• Wieslaw Kubis (Institute of Mathematics of the Academy of Sciences the Czech Republic)
• Aleksandra Kwiatkowska (University of Bonn, Germany)
• Veronica Martinez de la Vega (National Autonomous University of Mexico)
• Julien Melleray (Institut Camille-Jordan, Université Lyon 1, France)
• Jan van Mill (University of Amsterdam, Netherlands)
• Arnold Miller (University of Wisconsin–Madison, USA)
• Justin Moore (Cornell University, Ithaca, New York, USA)
• Chris Mouron (Rhodes College, Memphis, Tennessee, USA)
• Lionel Nguyen Van Thé (Institut de Mathématiques de Marseille, Université d’Aix–Marseille, France)
• Lex Oversteegen (University of Alabama at Birmingham, USA)
• Christian Rosendal (University of Illinois at Chicago, USA)
• Marcin Sabok (McGill University, Montreal, Canada)
• Slawomir Solecki (University of Illinois at Urbana–Champaign, USA)
• Lajos Soukup (Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences)
• Mikhail Tkachenko (Metropolitan Autonomous University, Iztapalapa, Mexico)
• Stevo Todorcevic (University of Toronto, Canada)
• Toshimichi Usuba (Kobe University, Japan)
• Benjamin Weiss (Hebrew University of Jerusalem, Israel)

### Scientific committee

• Bohuslav Balcar (Institute of Mathematics of the Academy of Sciences of the Czech Republic)
• Christina Brech (Departamento de Matemática, Universidade de São Paulo)
• K. P. Hart (Department of Mathematics, Delft University of Technology)
• Logan Hoehn (Department of Computer Science and Mathematics, Nipissing University)
• Petr Simon (Faculty of Mathematics and Physics, Charles University in Prague)
• Todor Tsankov (Institut de Mathématiques de Jussieu, Université Paris Diderot)
• Lyubomyr Zdomskyy (Kurt Gödel Research Center, University of Vienna)

### Organizing committee

• David Chodounský (Institute of Mathematics of the Academy of Sciences of the Czech Republic)
• Jan Starý (Department of Mathematics, Czech Technical University)
• Benjamin Vejnar (Faculty of Mathematics and Physics, Charles University in Prague)

David Chodounsky
Institute of Mathematics AS CR
Zitna 25, 115 67 Praha 1
Czech Republic
tel.: +420 222 090 715
email: chodounsky@math.cas.cz

## Dimitris Vlitas: Canonical equivalence relations on the topological Ramsey space FIN_k

Place: Fields Institute (Room 210)

Date: February 5, 2016 (13:30-15:00)

Speaker: Dimitris Vlitas

Title: Canonical equivalence relations on the topological Ramsey space $FIN_k$

Abstract: As an application of a more general theory recently developed, we give a complete list of all equivalence relations on barriers of the topological Ramsey space $FIN_k$, for all $k$.

## Alexander Melnikov: Constructive Abelian Groups

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 3 February 2016, 17:00 hrs

Room: S17#05-11, Department of Mathematics, NUS

Speaker: Alexander Melnikov

Title: Constructive Abelian Groups

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

Abstract:
First, we will briefly discuss the history of the old subject of computable
(constructive) Abelian groups, and how it fits into the modern computable
structure theory. Then we will discuss why a question of Goncharov on
Delta_n-categorical groups is central to the theory of computable Abelian
groups (terminology to be clarified), and what the question really asks.
Finally, we will briefly outline the key steps of my recent technical proof
showing such groups exist, at the level of an informal idea. (No solid
background in group theory is assumed.)

## Franklin Tall: Definable Versions of Hurewicz’s Conjecture that Menger Spaces are Sigma-compact

Place: Fields Institute (Room 210)

Date: January 29 , 2016 (13:30-15:00)

Speaker: Franklin Tall

Title: Definable Versions of Hurewicz’s Conjecture that Menger Spaces are Sigma-compact

Abstract: Hurewicz’s conjecture that Menger spaces are sigma-compact is false; it is true for analytic subspaces of Polish spaces and undecidable for other definable subspaces of Polish spaces. For non-metrizable spaces, analytic Menger spaces are sigma-compact, but projections of co-analytic spaces need not be. The co-analytic case may be undecidable, but is not yet settled. We have partial results. Our methods are a mix of non-metric descriptive set theory and Arhangel’skii’s work on generalized metric spaces.

## Wang Wei: Relative Definability of n-generic

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 27 January 2016, 17:00 hrs

Room: S17#05-11, Department of Mathematics, NUS

Speaker: Wang Wei

Title: Relative Definability of n-generic.

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

Abstract:
Jockusch proved that every 1-generic G is recursively
enumerable in some X strictly Turing below G and every
2-generic H is properly Sigma-2 in some Y strictly Turing below H.
So he conjectured that every n-generic G is properly
Sigma-n in some X strictly Turing below G.
Recently I confirmed Jockusch’s conjecture.
Here I will sketch the solution.

The paper is available at http://arxiv.org/pdf/1511.08875.pdf

## David Fernández Bretón: Gruff ultrafilters in the Random model

Thursday, January 28, 4:00-5:30 PM at CC Little 2502 (note the nonstandard building/room!!!):

A gruff ultrafilter (a concept introduced by van Douwen) is an ultrafilter on the rational numbers with a base of perfect subsets (where perfect means both closed (in the topology inherited from the usual Euclidean one from the reals) and crowded (without isolated points)). The main question regarding these objects is whether one can prove their existence in ZFC.Partial progress towards the answer of this question so far includes that their existence follows from cov(M)=c (van Douwen), from b=c (Coplakova-Hart) and holds in Sacks model (Millan) and in Miller’s model (F.B. and Hrusak). In this talk I will show a very recent piece of further partial progress: a proof that there exists a gruff ultrafilter in the Random model.

## Diana Ojeda: Topological partition relations for countable ordinals

Place: Fields Institute (Room 210)

Date: January 22 , 2016 (13:30-15:00)

Speaker: Diana Ojeda

Title: Topological partition relations for countable ordinals

Abstract:

The subject of topological partition relations provides answers to questions
of the following form: Given a topological space X and a subspace Y, is it
possible to reduce any given coloring of the pairs of elements of X to a simpler
coloring, by passing to a subspace homeomorphic to Y?

I will first present a survey of topological partition relations for countable
ordinals with the order topology. In many instances it is useful to represent
countable ordinals using families of finite sets. I will describe how to obtain
such representations; and will present results from a joint project with William
Weiss, where we obtain topological partition relations for ordinals below $\omega^2$ with the order topology.