## First Girona inner model theory conference, Girona, July 16-27 2018

The first Girona inner model theory conference will take place on July 16-27 at the Philosophy Department of the University of Girona, Catalonia.

The conference is a sequel to previous conferences on inner model theory in Münster, Palo Alto, Berkeley and Irvine. Once more, the meeting will draw together researchers and advanced students with an interest in inner model theory, in order to communicate and further explore recent work. There will be courses and single talks Monday-Friday, with 2 1/2 hours of lectures in the morning and 2 1/2 hours of lectures in the afternoon. This will leave ample time for problem sessions, informal seminars, and other interactions.

The conference is organized by Ralf Schindler (Münster), John Steel (Berkeley) and Joan Vergés (Girona). Please contact Ralf Schindler (rds@wwu.de) if you intend to participate.

## Two-year postdoctoral position in set theory and logic at NUS

The department of mathematics of the National University of Singapore (NUS) invites applications for a postdoctoral position in set theory and logic which will start in July 2018.

The logic group at NUS consists of 4 faculty members and a varying number of postdoctoral fellows working in set theory and recursion theory. The department of mathematics has about 60 faculty members whose expertise cover major areas of mathematical research. NUS is a leading global university centered in Asia which offers an environment conducive to active research. Salary and remuneration are internationally competitive.

Applicants should have a PhD degree in mathematics at the time of starting the job, and the focus of their research should be in set theory and logic, or closely related areas.
The duration of the position is for two years.
The selected applicant is expected to start on or after July 1, 2018. The exact starting date is negotiable.
The position carries no teaching load. However optional teaching opportunities are provided.

A complete application consists of the following:

• cover letter;
• CV and list of publications;
• Three reference letters (to be sent directly by the letter writers)

These materials are to be emailed to the address matrd@nus.edu.sg. Applicants should also arrange for three recommendation letters to be sent directly to the address matrd@nus.edu.sg.

Applications are accepted until the position is filled.

## Two talks: Aurichi and de Rancourt

The seminar meets on Wednesday February 7th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Time permitting, we will have two talks.

1. Leandro Aurichi — Some problems with products of Lindelöf spaces
Some problems about the preservation of the Lindelöf property on
products will be discussed.
2. Noé de Rancourt — Ramsey theory with and without pigeonhole principle
I will present an abstract infinite-dimensional Ramsey principle that doesn’t need any pigeonhole principle, and then I will compare the cases where the pigeonhole principle holds and the cases where it doesn’t, in a metamathematical way.

## Jing Zhang: Rado’s Conjecture and its Baire Version II

Mathematical logic seminar – Jan 30 2018
Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         Jing Zhang
Department of Mathematical Sciences
CMU

Title:     Rado’s Conjecture and its Baire Version II

Abstract:

Rado’s Conjecture is a reflection/compactness principle formulated by Todorčević, who also showed its consistency relative to the existence of strongly compact cardinals. One of its equivalent forms asserts that any nonspecial tree of height ω1 has a nonspecial subtree of size less or equal to ℵ1. Although it is incompatible with Martin’s Axiom, Rado’s Conjecture turns out to imply a lot of consequences of forcing axioms, for example Strong Chang’s Conjecture, failure of square principles, the semi-stationary reflection principle, the Singular Cardinal Hypothesis etcetera. In fact, almost all known consequences of Rado’s Conjecture are consequences of a weaker statement, the Baire version of it which asserts any Baire tree of height ω1 has a nonspecial subtree of size less or equal to ℵ1.

We will show that in the forcing extension by countable support iteration of Sacks forcing of strongly compact length, the Baire version of Rado’s Conjecture holds. Using a classical Mitchell style model, we show Rado’s conjecture along with not-CH does not imply ω2 has the super tree property, answering a question by Torres-Pérez and Wu. We will also see that in general the Baire version of Rado’s Conjecture does not imply Rado’s Conjecture.

## Stevo Todorcevic: P-ideal dichotomy and versions of Souslin Hypothesis

Place: Fields Institute (Room 210)

Date: January 26, 2018 (13:30-15:00)

Speaker: Stevo Todorcevic

Title: P-ideal dichotomy and versions of Souslin Hypothesis

Abstract: This is a joint work with B. kuzeljevic. This talk will be about the relationship of PID with various forms of SH such as, for example, the statement that all Aronszajn trees are $\mathbb{Q}$-embeddable.

## Dilip Raghavan: An application of PCF theory to cardinal invariants above the continuum

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 24 January 2018, 17:00 hrs

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

Speaker: Dilip Raghavan

Title: An application of PCF theory to cardinal invariants above the continuum

Abstract: It will be proved in ZFC that if kappa
is any regular cardinal greater than beth_omega, then
d(kappa) leq r(kappa). Here d(kappa) is the
smallest size of dominating family of functions from kappa
to kappa and r(kappa) is the smallest size of a family
of subsets of kappa which decide every other subset of kappa.
This result partially dualizes an earlier result
of myself and Shelah. The proof uses the revised GCH,
which is an application of PCF theory.
This is joint work with Shelah.

## Fulgencio Lopez: Adding Cohen reals also adds a capturing Construction Scheme

Place: Fields Institute (Room 210)

Date: January 19, 2018 (13:30-15:00)

Speaker: Fulgencio Lopez

Abstract: We show that adding $\kappa\geq \omega_1$ Cohen reals adds a capturing construction scheme.

## Jing Zhang: Rado’s Conjecture and its Baire Version

Mathematical logic seminar – Jan 23 2018
Time:     3:30pm – 4:30 pmRoom:     Wean Hall 8220

Speaker:         Jing Zhang
Department of Mathematical Sciences
CMU

Title:     Rado’s Conjecture and its Baire Version

Abstract:

Rado’s Conjecture is a reflection/compactness principle formulated by Todorčević, who also showed its consistency relative to the existence of strongly compact cardinals. One of its equivalent forms asserts that any nonspecial tree of height ω1 has a nonspecial subtree of size less or equal to ℵ1. Although it is incompatible with Martin’s Axiom, Rado’s Conjecture turns out to imply a lot of consequences of forcing axioms, for example Strong Chang’s Conjecture, failure of square principles, the semi-stationary reflection principle, the Singular Cardinal Hypothesis etcetera. In fact, almost all known consequences of Rado’s Conjecture are consequences of a weaker statement, the Baire version of it which asserts any Baire tree of height ω1 has a nonspecial subtree of size less or equal to ℵ1.

We will show that in the forcing extension by countable support iteration of Sacks forcing of strongly compact length, the Baire version of Rado’s Conjecture holds. Using a classical Mitchell style model, we show Rado’s conjecture along with not-CH does not imply ω2 has the super tree property, answering a question by Torres-Pérez and Wu. We will also see that in general the Baire version of Rado’s Conjecture does not imply Rado’s Conjecture.

## Clinton Conley: Unfriendly colorings of measure-preserving graphs of finite cost

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

Room:     Wean Hall 8220

Speaker:         Clinton Conley
Department of Mathematical Sciences
CMU

Title:     Unfriendly colorings of measure-preserving graphs of finite cost

Abstract:

We show that any measure-preserving Borel graph on a standard probability space with finite average degree admits a Borel unfriendly coloring on a conull set. This generalizes the results for group actions discussed last semester, and is joint work with Omer Tamuz.

## Osvaldo Guzman Gonzalez: On (1,w_1)-weakly universal functions

Place: Fields Institute (Room 210)

Date: January 12, 2018 (13:30-15:00)

Speaker: Osvaldo Guzman Gonzalez

Title: On (1,w_1)-weakly universal functions

Abstract: We will study a very weak notion of universality of functions in Sacks models. We will answer a question of Shelah and Steprans by showing that there are no (1,w_1)-weakly universal functions after adding uncountably many Sacks reals side by side.