2018
Apr
15

# Seminars

2018
May
22

2018
May
09

# Logic Seminar - Immanuel Benporat - "Arbault sets"

11:00am to 1:00pm

## Location:

Ross 63

Arbault sets (briefly, A-sets) were first introduced by Jean Arbault in the context of Fourier analysis. One of his major results concerning these sets,asserts that the union of an A-set with a countable set is again an A-set. The next obvious step is to ask what happens if we replace the word "countable" by א_1. Apparently, an א_1 version of Arbault's theorem is independent of ZFC. The aim of this talk would be to give a proof (as detailed as possible) of this independence result. The main ingredients of the proof are infinite combinatorics and some very basic Fourier analysis.

2017
Dec
13

# Logic seminar - Omer Mermelstein - "Template structures for the class of Hrushovski ab initio geometries"

11:00am to 1:00pm

## Location:

Math 209

Zilber's trichotomy conjecture, in modern formulation, distinguishes three flavours of geometries of strongly minimal sets --- disintegrated/trivial, modular, and the geometry of an ACF. Each of these three flavours has a classic ``template'' --- a set with no structure, a projective space over a prime field, and an algebraically closed field, respectively. The class of ab initio constructions with which Hrushovski refuted the conjecture features a new flavour of geometries --- non-modular, yet prohibiting any algebraic structure.

2018
May
23

# Logic Seminar - Alejandro Poveda Ruzafa - "A Magidor-like study of $C^{(n)}$-cardinals"

11:00am to 1:00pm

## Location:

Ross 63

The notion of reflection plays a central role in modern Set Theory since the descovering of the well-known Lévy and Montague \textit{Reflection principle}. For any $n\in\omega$, let $C^{(n)}$ denote the class of all ordinals $\kappa$ which correctly interprets the $\Sigma_n$-statements of the universe, with parametes in $V_\kappa$.

2017
Mar
15

# Logic seminar - Rizos Sklinos, "Non-equational stable groups"

4:00pm to 6:00pm

## Location:

Ross 70

Non-equational stable groups.
Speaker: Rizos Sklinos
Abstract: The notion of equationality has been introduced by Srour and further
developed by Pillay-Srour. It is best understood intuitively as a notion
of Noetherianity on instances of first-order formulas. A first-order
theory is equational when every first-order formula is equivalent to a
boolean combination of equations.
Equationality implies stability and for many years these two notions were
identified, as only an "artificial" example of Hrushovski (a tweaked
pseudo-space) was witnessing otherwise. Recently Sela proved that the

2017
May
29

# Logic seminar - Ur Yaar, "A Toy Multiverse"

2:00pm to 4:00pm

## Location:

Shprinzak 101

We will present briefly the "multiverse view" of set theory, advocated by Hamkins, that there are a multitude of set-theoretic universes, and not one background universe, and his proposed "Multiverse Axioms". We will then move on to present the main result of Gitman and Hamkins in their paper "A natural model of the multiverse axioms" - that the countable computably saturated models of ZFC form a "toy model" of the multiverse axioms.

2018
Mar
21

# Logic Seminar - Jorge Julián Prieto Jara - "Differentially closed fields and quasiminimality"

11:00am to 1:00pm

## Location:

Ross 63

Zilber introduced quasi-minimal classes to generalize the model theory of pseudo exponential
fields. They are equipped with a pregeometry operator and satisfy interesting properties such
as having only countable or co-countable definable sets. Differentially closed fields of
characteristic 0, rich examples of a \omega-stable structures, are good candidates to be
quasiminimal. The difficulty is that a differential equation may have uncountably many
solutions, and thus violate the countable closure requirement of quasiminimal structures.

2017
Nov
29

# Logic Seminar - Isabel Muller - "Zil'bers Conjecture and Building-like Geometries"

11:00am to 1:00pm

In an attempt to classify the geometries arising in strongly minimal sets, Zil'ber conjectured them to split into three different types: Trivial geometries, vector space-like geometries and field-like geometries. Soon after, Hrushovski refuted this conjecture while introducing a new construction method, which has been modified and used a lot ever since.

2018
Jun
20

# Logic Seminar - Daniel Palacin - "On definable Bohr compactifications of ultraproducts of finite groups"

11:00am to 1:00pm

## Location:

Ross 63

Abstract: In this talk I will discuss some suitable definable Bohr compactification of an ultraproduct of finite groups, and relate it to ultra quasirandom groups.

2017
Apr
19

# Logic seminar- Shimon Garti, "Forcing axioms and saturated ideals"

4:00pm to 6:00pm

## Location:

Ross 70

Abstract: Paul Larson proved that under Martin's axiom and large continuum there are no Laver ideals over aleph_1. He asked about weakly Laver ideals under some forcing axiom.
We shall address two issues:
1. Under Martin's axiom and the continuum is above aleph_2, there are no weakly Laver ideals over aleph_1..
2. Under Baumgartner's axiom, the parallel of Larson's theorem holds for ideals over aleph_2.

2017
Jan
11

# Logic seminar - Daniel Palacin, "Superrosy division rings"

10:00pm to 12:00am

## Location:

Ross 70

In this talk we analyze superrosy division rings, i.e. division rings which admit a well-behaved ordinal valued rank function on definable sets that behaves like a rudimentary notion of dimension. Examples are the quaternions, superstable division rings (which are known to be algebraically closed fields) and more generally supersimple division rings which are commutative.

2018
Jan
24

# Logic Seminar - Vadim Kulikov - Borel Reducibility in Generalised Descriptive Set Theory"

11:00am to 1:00pm

## Location:

Ross 63

I will review some recent results in the Borel reducibility on uncountable cardinals of the Helsinki logic group.
Borel reducibility on the generalised Baire space \kappa^\kappa for uncountable \kappa is defined analogously to that for \kappa=\omega. One of the corollaries of this work is that under some mild cardinality assumptions on kappa, if T1 is classifiable and T2 is unstable or superstable with OTOP, then the ISOM(T1) is continuously reducible ISOM(T2) and ISOM(T2) is not Borel reducible to ISOM(T1).

2017
Nov
15

# Logic Seminar - Shimon Garti - " Length of Boolean algebras"

11:00am to 1:00pm

## Location:

Math 209

We shall prove that there is a sequence of Boolean algebras for which the ultraproduct of the lengths divided by an ultrafilter is strictly less than the length of the product algebra.
This is a joint work with Saharon Shelah.

2018
Jun
06

# Logic Seminar - Gabriel Conant - "Local NIP group theory and pseudofinite groups"

11:00am to 1:00pm

## Location:

Ross 63

Much of the early development of model theoretic stability theory was motivated by stable groups, which include algebraic groups as guiding examples. Later work of Hrushovski and Pillay showed that many tools from stable group theory can be adapted to the local setting, where one works around a single stable formula rather than a stable theory. More recently, groups definable in NIP theories have been intensively studied, bringing back the importance of measures in model theory. On the other hand, local NIP group theory is not as well understood.