## Randall Holmes: Constructing proofs with a dependent type checker

Tuesday, October 25 from 3 to 4pm
Room: MB 124
Speaker: Randall Holmes (BSU)
Title: Constructing proofs with a dependent type checker

Abstract: I’ll discuss my latest theorem proving work, and present examples. I’ll explain what dependent type theory is and how a type checker for a dependent type theory can be a theorem prover. The talk should be accessible to students.

## David J. Fernández Bretón: Strong failures of higher analogs of Hindman’s theorem, III

Thursday, October 27, 2016, from 4 to 5:30pm
East Hall, room 3096

Speaker: David J. Fernández Bretón (University of Michigan)

Title: Strong failures of higher analogs of Hindman’s theorem, III

Abstract:

Assuming the Continuum Hypothesis, Hindman, Leader and Strauss recently exhibited a colouring of the real line with two colours such that, for every uncountable set of reals, the collection of pairwise sums of these reals is panchromatic. We will show a few generalizations of these results, obtaining colourings both of the real line, and of other abelian groups, in many colours, satisfying similar anti-Ramsey-theoretic properties. This is talk number 3 out of n (where n is still TBD), and its contents are joint work with Assaf Rinot.

## Sanjay Jain: Deciding parity games in quasipolynomial time

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 26 October 2016, 17:00 hrs

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

Speaker: Sanjay Jain

Title: Deciding parity games in quasipolynomial time

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

Parity games are games on finite graphs where each
node has a value. Two players, Anke and Boris,
move alternately a marker through the graph
and plays between the two players have infinite
duration. One determines the winner of such an infinite
play by taking the largest value of a node which is visited
infinite often; if this value is even then the first player
Anke wins else the second player Boris wins.

An important question is to determine the player who
has a winning strategy in such games. One evaluates such
algorithms in terms of the number n of nodes and number
m of colours and other possible parameters. Prior work
has given algorithms with runtime O(n^{m/3}) and
O(n^{Sqrt(n)}). The talk will present an improved
quasipolynomial algorithm with runtime O(n^{log(m)+8}).
Furthermore, if m < log(n), one can determine the winner
in time O(n^5); thus the problem is fixed-parameter
tractable, bringing it from the prior known complexity
class XP into FPT.

This is joint work with Cristian Calude, Bakhadyr
Khoussainov, Li Wei and Frank Stephan. The paper
is available at

http://www.comp.nus.edu.sg/~sanjay/paritygame.pdf

## Franklin Tall: Arhangel’skii’s Lindelof points- $G_{\delta}$ problem

Place: Fields Institute (Room 210)

Date: October 21st, 2016 (13:30-15:00)

Speaker: Franklin Tall

Title: Arhangel’skii’s Lindelof points- $G_{\delta}$ problem

Abstract: My claim of a solution was premature. I will discuss the history of the
problem, introduce n-dowments and the Mitchell collapse, and prove some results that could lead to a solution. If time permits, I will correct and improve a result I talked about last summer, proving that if every Hurewicz projective set of reals in sigma-compact, then there is an inaccessible in an inner model.

## David Chodounsky: Combinatorial properties of the Mathias-Prikry forcing

Tuesday, October 25, 2016, 17:15
Wrocław University of Technology, 215 D-1

Speaker: David Chodounsky (Czech Academy of Sciences)

Title: Combinatorial properties of the Mathias-Prikry forcing

Abstract:

I will review basic fact and results about the Mathis-Prikry forcing and I will present and prove sufficient condition for genericity of reals with respect to this poset. Time permitting, further connections of parameters of the forcing with its properties will be explored.

# Set theory conference

## July 29–Aug 04, 2017

Organizers: Menachem Magidor (Jerusalem), Ralf Schindler (Münster), John Steel (Berkeley), W. Hugh Woodin (Harvard)

## David J. Fernández Bretón: Strong failures of higher analogs of Hindman’s theorem, II

Thursday, October 20, 2016, from 4 to 5:30pm
East Hall, room 3096

Speaker: David J. Fernández Bretón (University of Michigan)

Title: Strong failures of higher analogs of Hindman’s theorem, II

Abstract:

(One of the versions of) Hindman’s theorem states that, whenever we partition an infinite abelian group G in two cells, there exists an infinite subset X of G such that the set FS(X) consisting of all sums of finitely many distinct elements of X is entirely contained within one of the cells of the partition. In this talk we will show that, when one attempts to replace both instances of “infinite” with “uncountable” in the theorem above, the resulting statement is not only false, but actually very false. This is talk 2 out of n (where n is a still unknown countable ordinal greater than or equal to 2). Joint work with Assaf Rinot.

## James Cummings: Cardinal invariants of the continuum

Mathematical logic seminar – October 18 2016
Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         James Cummings
Department of Mathematical Sciences
CMU

Title:     Cardinal invariants of the continuum

Abstract:

The cardinal invariants of the continuum are cardinals which measure properties of the continuum more subtle than its cardinality. We will define some of the important ones and discuss their properties.

Note: This seminar will provide some background for Mayanthe Malliaris’ forthcoming Appalachian Set Theory workshop on November 5, see workshop web page at http://www.math.cmu.edu/users/jcumming/Appalachian/malliaris_cmu_2016.html for details.

## 10th Young Set Theory Workshop, Edinburgh, July 10-14, 2017

The 10th installment of the Young Set Theory Workshop will take place July 10-14, 2017 in Edinburgh.

### Organisers

Name Institution
Brooke-Taylor, Andrew University of Leeds
Dimopoulos, Stamatis University of Bristol
Welch, Philip University of Bristol

#### Invited local speakers:

We shall consider a couple of properties of $\sigma$-ideals and relations between them. Namely we will prove that $\mathfrak c$-cc $\sigma$-ideals are tall, Weaker Smital Property implies that every Borel $\mathcal I$-positive set contains a witness for non($\mathcal I$) as well, as satisfying ccc and Fubini Property. We give also a characterization of nonmeasurability of $\mathcal I$-Luzin sets and prove that the ideal $[{\mathbb R}]^{\leq\omega}$ does not posses the Fubini Property using some interesting lemma about perfect sets.