## Ashutosh Kumar: Avoiding rational distances in plane

Place: Bahen Centre (Room BA 2135)

Date: August 26th, 2016 (13:30-15:00)

Speaker: Ashutosh Kumar

Title: Avoiding rational distances in plane

Abstract: We show that every graph of countable coloring number on a set of reals has an everywhere non meager independent set. In particular, every set of points in the plane has an everywhere non meager subset no two of whose points are at a rational distance.

## Secil Tokgoz: OCA and Menger’s Conjecture

Place: Bahen Centre (Room BA2135)

Date: August 19th , 2016 (13:30-15:00)

Speaker: Secil Tokgoz

Title: OCA and Menger’s Conjecture

Abstract: It was previously known that Projective Determinacy implies Menger projective sets of reals are sigma-compact. The hypothesis has considerable large cardinal strength; we are able to reduce the conclusion’s consistency strength to that of an inaccessible. In fact this is an equiconsistency result. We derive the conclusion from a perfect strengthening of OCA. Equiconsistency is proved by an argument involving the dominating number and the Covering Lemma. This is joint work by Secil Tokgoz, Frank Tall and S. Todorcevic.

## Ding Longyun: On generalisation of the Jayne-Rogers Theorem

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 31 August 2016, 17:00 hrs

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

Speaker: Ding Longyun

Title: On generalisation of the Jayne-Rogers Theorem

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

Let X,Y be separable metrizable spaces with X analytic, and let
f be function from X to Y. We say f is Sigma-m-n if, for any
Sigma-n subset A of Y, the preimage of A under f is Sigma-m.
A theorem of Jayne-Rogers shows that, a function f is Sigma-2-2 iff
X can be decomposed into countably many Sigma-2 subsets such that
f is continuous on each of these subsets. In this talk, we will
generalize this theorem to Sigma-m-n with n leq m =3 .
We also survey the history of the study on decomposing Borel functions.

## Mehrdad Maleki: Introduction to information systems

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 24 August 2016, 17:00 hrs

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

Title: Introduction to information systems

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

Abstract:
Information systems are another approach to domain theory which was
introduced by Dana Scott in 1982. Information systems give
information about possible elements of domains by means of some kind
of logical systems. Although Scott shows that information systems and
algebraic domains are equivalent, so it seems information systems give
no new information about domains, however, the former approach is more
constructive. In this talk, we will introduce information systems and
show information systems are a kind of observable properties of
domains. At the end application of information systems in Computer
Science will be introduced.

## Appalachian Set Theory workshop: Maryanthe Malliaris, November 5, 2016

The next meeting of the Appalachian Set Theory workshop series will take place
at CMU and may be of interest to the Pittsburgh logic community.

Maryanthe Malliaris will lead a workshop on “Cofinality spectrum
problems: p, t, and model theory”.

For details please see the workshop web page at http://www.math.cmu.edu/users/jcumming/Appalachian/malliaris_cmu_2016.html

The Appalachian Set Theory workshop series is supported by the National
Science Foundation.

## Chong Chitat: 1-generic degrees bounding minimal degrees

Invitation to the Logic Seminar at the National University of Singapore

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

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

Speaker: Chong Chitat

Title: 1-generic degrees bounding minimal degrees

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

Abstract:
1-generic sets are constructed using Cohen forcing while
sets of minimal degree are obtained via perfect set forcing. These are
two incompatible techniques ensuring that the class of 1-generic
degrees is disjoint from the class of minimal degrees. The ordering
relation between members of these two classes is a problem that has
been investigated since the late 1970’s. In this talk we discuss it
from the reverse mathematics point of view.

## Frank Stephan: On block pumpable languages

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, Wednesday 10 Aug 2016, 17:00 hrs

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

Speaker: Frank Stephan

Title: On block pumpable languages

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

Abstract:
Call a language L block pumpable iff there is a constant p>1 such
that for every splitting of a word in the language L into p+1 blocks,
one can find a subword consisting of an interval of the interior blocks
such that each modified word obtained by repeating or omitting this
subword is also in the language L. Such subwords are called pump.
Ehrenfeucht, Parikh and Rozenberg showed that a language is regular
iff the language and its complement are both block pumpable. The aim
of this paper is to provide some evidence that beyond this
characterisation, block pumpable languages are a notion which is
interesting in its own right. It will be shown that block pumpable
languages satisfy natural closure properties: The intersection of
two block pumpable languages is block pumpable, the union of two
block pumpable languages is block pumpable and the image of block
pumpable languages under a transduced mapping is block
pumpable. However, block pumpable languages are not closed under
complement and Kleene star. Furthermore, block pumpable languages
satisfy the condition that one can pump them several times, that
is, for each k and each sufficiently large number p(k) and
every splitting of a word into p(k) parts, one can find k disjoint
pumps in the word which can be pumped independently. The growth-rate
(number of words up to given length) of every non-regular pumpable
language is exponential. One can define block pumpable relations
and structures and show that the existential theory of such a
structure is decidable and that an alternation of quantifiers
destroys decidability.

The talk follows the paper “On block pumpable languages”
by Christopher Chak, Rusins Freivalds, Frank Stephan
and Henrietta Tan, which contains contains results from the FYP
of Christopher Chak and Henrietta Tan; the paper appeared in
Theoretical Computer Science 609:272-285, 2016. Furthermore, the talk
also presents results from the FYP of Jonathan Sung. The talk had
been presented at the conference “Computability, Randomness and
Applications” in Luminy, France.

## Miguel Angel Mota: Measuring together with the continuum large

Place: TBD

Date: July 15th , 2016 (13:30-15:00)

Speaker: Miguel Angel Mota

Title: Measuring together with the continuum large

Abstract:  Measuring, as defined by Justin Moore, says that for every sequence $(C(\delta))_{\delta<\omega_1}$ with each $C(\delta)$ being a closed subset of $\delta$ there is a club $C\subseteq\omega_1$ such that for every $\delta \in C$, a tail of $C\cap\delta$ is either contained in or disjoint from $C(\delta)$. We answer a question of Justin Moore by building a forcing extension satisfying measuring together with $2^{\aleph_0}>\aleph_2$.

## 6th European Set Theory Conference, Budapest, July 3-7, 2017

ANNOUNCEMENT

We are pleased to announce that the 6th European Set Theory Conference (6ESTC) of the European Set Theory Society will be organized in Budapest, at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences, next year, July 3 – 7, 2017. (Date of arrival: July 2, date of departure: July 8.)

Local Organizing Committee:
L. Soukup (chair), M. Elekes (secretary), I. Juhász, V. Kiss, G. Sági, D. Sziráki, Z. Vidnyánszky.

Program Committee:
I. Juhász (chair, Budapest), T. Bartoszynski (Washington, DC), M. Džamonja (Norwich), S. D. Friedman (Vienna), W. Kubiś (Kielce and Prague), M. Magidor (TBC, Jerusalem), H. Mildenberger (Freiburg).

Homepage of the meeting:

If you are interested in attending this meeting, we kindly ask you to fill out the following very short form:
https://goo.gl/Fl5ssU

We also encourage you advertise this meeting to anyone who you think may be interested, especially to potentially interested students and young set theorists.

With best regards,
The Organizers

## BEST 2016 slides

The 23rd BEST conference was held June 15–16 in San Diego, CA.

Shehzad Ahmed – Jonsson cardinals and pcf theory
Liljana Babinkostova – A weakening of the closure operator
Kyle Beserra – On the conjugacy problem for automorphisms of countable regular trees
Erin Carmody – Killing them softly
William Chan – Every analytic equivalence relation with all Borel classes is Borel somewhere
John Clemens – Relative primeness of equivalence relations
Paul Corazza – The axiom of infinity, quantum field theory, and large cardinals
Cody Dance – Indiscernibles for $L[T_2,x]$
Natasha Dobrinen – Ramsey spaces coding universal triangle-free graphs and applications to Ramsey degrees
Paul Ellis – A Borel amalgamation property
Monroe Eskew – Rigid ideals
Daniel Hathaway – Disjoint Borel functions
Jared Holshouser – Partition properties for non-ordinal sets under the axiom of determinacy
Paul McKenney – Automorphisms of \$\mathcal P(\lambda)/\mathcal I_\kappa
Kaethe Minden – Subcomplete forcing and trees
Daniel Soukup – Orientations of graphs with uncountable chromatic number
Simon Thomas – The isomorphism and bi-embeddability relations for finitely generated groups
Douglas Ulrich – A new notion of cardinality for countable first order theories
Kameryn Williams – Minimal models of Kelley-Morse set theory
Martin Zeman – Master conditions from huge embeddings