## Ari Brodsky: Custom-made Souslin trees

Place: Fields Institute (Room 210)

Date: May 2nd , 2016 (13:30-15:00)

Speaker: Ari Brodsky

Abstract:  We propose a parametrized proxy principle from which $\kappa$-Souslin trees with various additional features can be constructed, regardless of the identity of $\kappa$. We then introduce the microscopic approach, which is a simple method for deriving trees from instances of the proxy principle. As a demonstration, we give a construction of a coherent $\kappa$-Souslin tree that applies also for $\kappa$ inaccessible.

## Barnabas Farkas: Towers in filters and related problems

Tuesday, May 10, 2016, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Barnabas Farkas (University of Vienna)

Title: Towers in filters and related problems

Abstract:

I am going to present a survey on my recently finished joint work with J. Brendle and J. Verner. In this paper we investigated which filters can contain towers, that is, a $\subseteq^*$-decreasing sequence in the filter without any pseudointersection (in $[\omega]^\omega$). I will present Borel examples which contain no towers in $\mathrm{ZFC}$, and also examples for which it is independent of $\mathrm{ZFC}$. I will prove that consistently every tower generates a non-meager filter, in particular (consistently) Borel filters cannot contain towers. And finally, I will present the “map” of logical implications and non-implications between (a) the existence of a tower in a filter $\mathcal{F}$, (b) inequalities between cardinal invariants of $\mathcal{F}$, and (c) the existence of a peculiar object, an $\mathcal{F}$-Luzin set of size $\geq\omega_2$.

## Andy Zucker: Algebra in the Samuel compactification II

Mathematical logic seminar – April 19 2016
Time:     12:30 – 13:30

Room:     Wean Hall 8220

Speaker:         Andy Zucker
Department of Mathematical Sciences
CMU

Title:     Algebra in the Samuel compactification II

Abstract:

To every topological group G we can associate its Samuel compactification (S(G), 1). This is the largest point-transitive G-flow according to a suitable universal property. Using the universal property, we can endow S(G) with the structure of a compact left-topological semigroup. While the algebraic properties of S(G) are an active area of research for G a countable discrete group, less attention has been paid to other topological groups. In this talk, we will discuss a method of characterizing S(G) when G is an automorphism group of a countable structure. We will then take a closer look at the case G = S∞ and answer several questions about the algebraic structure of S(G). This is joint work with Dana Bartošová.

## Matthias Baaz: Towards a proof theory of analogical reasoning

Invitation to the Logic Seminar at the National University of Singapore

Date: Monday, 25 April 2016, 15:00 hrs

Room: S17#04-06, Department of Mathematics, NUS

Speaker: Matthias Baaz, Technische Universitaet Wien

Title: Towards a proof theory of analogical reasoning

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

In this lecture we compare three types of analogies based on
generalizations and their instantiations:

1. Generalization w.r.t. to invariant parts of proofs, for example,
graphs of rule applications.
2. Generalization w.r.t. to an underlying meaning: Here proofs and
calculations are considered as trees of formal expressions.
We analyze the well-known calculation attributed to Euler
demonstrating that the 5th Fermat number is compound, i.e.,
that Fermat’s claim is false, that all Fermat numbers are primes.
3. Generalization w.r.t. to the premises of a proof: This type of
analogies is especially important for juridical reasoning.

## Juris Steprans: Graph embedding and the P-ideal dichotomy

Place: Fields Institute (Room 210)

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

Speaker: Juris Steprans

Title: Graph embedding and the P-ideal dichotomy

Abstract: I will discuss a family of proofs of the consistency of a universal graph on $\omega_1$ with the failure of CH that rely on iterating reals and using the P-ideal dichotomy.

## Ioannis Souldatos: The Hanf number for Scott sentences of computable structures.

Thursday, April 21, 2016, 4:00–5:30 PM, 3088 East Hall.

We will prove the following two theorems:
Theorem 1: Let A be a computable structure for a computable vocabulary \tau, and let \sigma be a Scott sentence for A. If \sigma has models of cardinality \beth_\alpha for all \alpha<\omega_1^{CK}, then it has models of all infinite cardinalities.
Theorem 2: (Using Kleene’s O:) For every ordinal notation a\in O, there exists a computable structure A, such that A characterizes \beth_{|a|}, where |a| is the ordinal defined by a.
Combining the above two theorems we obtain that the Hanf number for Scott sentences of computable structures is equal to \beth_{\omega_1^{CK}}. This answers a question of Sy D. Friedman.

## Marion Scheepers: Ramsey theory and the Borel Conjecture

Boise Set Theory Seminar
Wednesday, April 20 from 3 to 4pm
Room: MB 124
Speaker: Marion Scheepers (BSU)

Title: Ramsey theory and the Borel Conjecture

Abstract: The Borel Conjecture states that certain measure zero sets of real numbers are countable. This statement can be converted to a statement that a set of real numbers is one of these special measure zero sets if, and only if, a special associated structure satisfies a version of Ramsey’s Theorem. We discuss this connection, and explore a range of statements equivalent to the alluded to version of Ramsey’s Theorem.

## Andy Zucker: Algebra in the Samuel compactification II

Mathematical logic seminar – April 19 2016
Time:     12:30 – 13:30

Room:     Wean Hall 8220

Speaker:         Andy Zucker
Department of Mathematical Sciences
CMU

Title:     Algebra in the Samuel compactification II

Abstract:

To every topological group G we can associate its Samuel compactification (S(G), 1). This is the largest point-transitive G-flow according to a suitable universal property. Using the universal property, we can endow S(G) with the structure of a compact left-topological semigroup. While the algebraic properties of S(G) are an active area of research for G a countable discrete group, less attention has been paid to other topological groups. In this talk, we will discuss a method of characterizing S(G) when G is an automorphism group of a countable structure. We will then take a closer look at the case G = S∞ and answer several questions about the algebraic structure of S(G). This is joint work with Dana Bartošová.

## Francisco Guevara: Analytic group topologies

Place: Fields Institute (Room 210)

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

Speaker: Francisco Guevera

Title: Analytic group topologies

Abstract: We study the effective version Malykhin’s question about the metrizability of (countable) Frechet groups and its natural generalization to metrizability of (countable) sequential groups of higher sequential order. A countable topological space $(X,\tau)$ is analytic if $\tau$ is analytic as a subset of the Cantor set $2^X$. By effective we mean the group topology is analytic. A space is sequential if all sequentially closed sets are closed. In sequential spaces, the sequential order is defined as the minimal ordinal $\alpha$ so that the closure of every set is obtained by applying the operation of adding limit points $\alpha$-many times. A sequential space has order $1$ iff it is Frechet. The results presented in the talk come from some works of A. Shibakov,  S. Todorcevic, and C. Uzcategui.

## 1st Irvine Conference on Descriptive Inner Model Theory and HOD Mice, July 18-29 2016

1st Irvine Conference on Descriptive Inner Model Theory and HOD Mice

July 18 — 29, 2016
Department of Mathematics, UC Irvine

Supported by: NSF Grants DMS-x, DMS- 1044150, DMS-y, and UCI CORCL

Organizers: Grigor Sargsyan (Rutgers), Nam Trang (Irvine), Martin Zeman
(Irvine)

This workshop is a sequel to a series of conferences and workshops on
descriptive inner model theory including 1st Conference on the core model
induction and hod mice that was held in Münster (FRG), July 19 — August
06, 2010, the 2nd Conference on the core model induction and hod mice that
was held in Münster (FRG), August 08 — 19, 2011, the AIM Workshop on
Descriptive Inner Model Theory held in Palo Alto (CA), June 02 — 06,
2014, and to the Conference on Descriptive Inner Model Theory, held in
Berkeley (CA) June 09 — 13, 2014, and the 3rd Conference on the core
model induction and hod mice, held in Münster (FRG), July 20 — 31, 2015.

The main purpose of the workshop is to disseminate and communicate results
and recent development in descriptive inner model theory and related
subjects. The workshop consists of single talks by experts in the field on
their recent work as well as lectures aimed at advanced graduate students
interested in inner model theory and related fields.

Following past workshops, the first week of the workshop meets M–F; each
day consists of 4 lectures (each is 75 minutes long), 2 in the morning and
2 in the afternoon. Between the lectures, we will leave plenty of time for
discussions, lunch, and informal seminars. The second week will be more
informal; as in the past, the topics and speakers for the second week will
be decided during the first week of the meeting.

All lectures will take place in Natural Scienes II building, room 1201.
map

The organizers gratefully acknowledge the financial support from the
National Science Foundation (NSF).