## Rick Statman: Completeness of BCD for an operational semantics; forcing for proof theorists

Mathematical logic seminar – Feb 13 2018
Time: 3:30pm – 4:30 pm

Room: Wean Hall 8220

Speaker: Rick Statman
Department of Mathematical Sciences
CMU

Title: Completeness of BCD for an operational semantics; forcing for proof theorists

Abstract:

Intersection types provide a type discipline for untyped λ-calculus. The formal theory for assigning intersection types to lambda terms is BCD (Barendregt, Coppo, and Dezani). We show that BCD is complete for a natural operational semantics. The proof uses a primitive forcing construction based on Beth models (similar to Kripke models).

## Zach Norwood: Coding along trees and remarkable cardinals

Time: Mon, 02/12/2018 – 4:00pm – 5:30pm
Location: RH 440R

Speaker: Zach Norwood (UCLA)

Title: Coding along trees and remarkable cardinals

Abstract. A major project in set theory aims to explore the connection between large cardinals and so-called generic absoluteness principles, which assert that forcing notions from a certain class cannot change the truth value of (projective, for instance) statements about the real numbers. For example, in the 80s Kunen showed that absoluteness to ccc forcing extensions is equiconsistent with a weakly compact cardinal. More recently, Schindler showed that absoluteness to proper forcing extensions is equiconsistent with a remarkable cardinal. (Remarkable cardinals will be defined in the talk.) Schindler’s proof does not resemble Kunen’s, however, using almost-disjoint coding instead of Kunen’s innovative method of coding along branchless trees. We show how to reconcile these two proofs, giving a new proof of Schindler’s theorem that generalizes Kunen’s methods and suggests further investigation of non-thin trees.

## David J. Fernández Bretón: Models of set theory with union ultrafilters and small covering of meagre

Thursday, February 15, 2018, from 4 to 5:30pm
East Hall, room 3088

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

Title: Models of set theory with union ultrafilters and small covering of meagre

Abstract:

Union ultrafilters are ultrafilters that arise naturally from Hindman’s finite unions theorem, in much the same way that selective ultrafilters arise from Ramsey’s theorem, and they are very important objects from the perspective of algebra in the Cech–Stone compactification. The existence of union ultrafilters is known to be independent from the ZFC axioms (due to Hindman and Blass–Hindman), and is known to follow from a number of set-theoretic hypothesis, of which the weakest one is that the covering of meagre equals the continuum (this is due to Eisworth). I will show that such hypothesis is not a necessary condition, by exhibiting a number of different models of ZFC that have a covering of meagre strictly less than the continuum, while at the same time satisfying the existence of union ultrafilters.

## Wang Wei: Combinatorics and Probability in First and Second Order Arithmetic

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 14 February 2018, 17:00 hrs

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

Speaker: Wang Wei

Title: Combinatorics and Probability in First and Second Order Arithmetic

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

Abstract:
Recent years see emergence of connections between the reverse mathematics
of Ramsey theory and computable measure theory or algorithmic randomness.
Here we consider two simple propositions in measure theory which have
interesting connections to the reverse mathematics of Ramsey theory. The
first is that every set X in Cantor space of positive Lebesgue measure is
non-empty. If X is assumed to be effectively closed then this is the
well-known axiom WWKL-0. However, if X is allowed to be a
little wilder and the proposition is twisted a bit, then it could help in
understanding the first order theory of some Ramseyan theorems. The second
is that every set X in Cantor space of positive measure has a perfect
subset. This proposition is somehow related to a tree version of Ramsey's
theorem. But unlike the first one, it is not familiar to people either in
algorithmic randomness or reverse mathematics.



## 2017 North American ASL Meeting, Illinois, March 20-23, 2017

### 2018 North American Annual Meeting

#### Invited Speakers:

##### Plenary Speakers:

JC Beall, University of Connecticut
(TBA)

A. Chernikov, University of California at Los Angeles
(Local distality and distal parts of stable theories)

B. Hart, McMaster University
(In defense of ultraproducts)

J. Knight, University of Notre Dame
(Roots of polynomials in generalized power series)

R. Nagloo, Bronx Community College
(Model theory and classical differential equations)

D. Sinapova, University of Illinois at Chicago
(Stronger tree properties and the SCH)

S. Solecki, University of Illinois at Urbana-Champaign
(Fra\”iss\’e limits and compact spaces)

A. Weiermann, Ghent University, Belgium
(Generalized Goodstein sequences and notation systems for finite numbers)

##### Tutorial:

A. Marks, University of California at Los Angeles
(Descriptive set theory and geometric paradoxes)

T. Slaman, University of California at Berkeley
(Recursion theory and Diophantine approximation)

##### Special Sessions:
• Computability (L. Bienvenu and K. Lange)
• Logic and Philosophy (C. Franks)
• Model Theory (J. Freitag and J. Marikova)
• Proof Theory (H. Towsner)
• Set Theory (D. Sinapova and A. Tserunyan)

## Frank Tall: Co-analytic spaces, K-analytic spaces, and definable versions of Menger’s conjecture

Place: Fields Institute (Room 210)

Date: February 9, 2018 (13:30-15:00)

Speaker: Frank Tall

Title: Co-analytic spaces, K-analytic spaces, and definable versions of Menger’s conjecture

Abstract: I will not assume knowledge from my previous talks on this subject. We define co-K-analytic spaces and provide evidence that this is the “correct generalization” of ‘co-analytic’ to non-metrizable spaces. As before, we view the classic work of Rogers and Jayne on analytic sets through the lens of

Arhangel’skii’s work on generalized metric spaces, while we investigate the question of whether definable Menger spaces are sigma-compact.

## David Belanger: Randomness versus induction

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 07 February 2018, 17:00 hrs

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

Speaker: David Belanger

Title: Randomness versus induction

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

We look at some recent work towards finding the axiomatic strength of the
statement: There is a Martin-Loef random set of natural numbers.

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

Place: Fields Institute (Room 210)

Date: February 2, 2018 (13:30-15:00)

Speaker: Stevo Todorcevic

Title: P-ideal dichotomy and versions of Souslin Hypothesis, continued

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 Q-embeddable.

## 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.