2018
Apr
11

# Logic Seminar - Shahar Oriel - "The infinite random simplicial complex"

11:00am to 1:00pm

## Location:

Ross 63

This talk will be a review of a paper by Andrew Brooke-Taylor and Damiano Testa:

Edmond J. Safra Campus The Hebrew University of Jerusalem

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2018
Apr
11

11:00am to 1:00pm

Ross 63

This talk will be a review of a paper by Andrew Brooke-Taylor and Damiano Testa:

2017
Mar
01

4:00pm to 6:00pm

Ross 70

Weak Prediction Principles

Speaker: Yair Hayut

Abstract: Jensen's diamond is a well studied prediction principle. It holds in L (and other core models), and in many cases it follows from local instances of GCH.

In the talk I will address a weakening of diamond (due to Shaleh and Abraham) and present Abraham's theorem about the equivalence between weak diamond and a weak consequence of GCH. Abraham's argument works for successor cardinals. I will discuss what is known and what is open for inaccessible cardinals.

Speaker: Yair Hayut

Abstract: Jensen's diamond is a well studied prediction principle. It holds in L (and other core models), and in many cases it follows from local instances of GCH.

In the talk I will address a weakening of diamond (due to Shaleh and Abraham) and present Abraham's theorem about the equivalence between weak diamond and a weak consequence of GCH. Abraham's argument works for successor cardinals. I will discuss what is known and what is open for inaccessible cardinals.

2017
Jul
26

2:00pm to 4:00pm

Ross 70

Dependent theories have now a very solid and well-established collection of results and applications. Beyond first order, the development of "dependency" has been rather scarce so far. In addition to the results due to Kaplan, Lavi and Shelah (dependent diagrams and the generic pair conjecture), I will speak on a few lines of current research around the extraction of indiscernibles for dependent diagrams and on various forms on dependence for abstract elementary classes. This is joint work with Saharon Shelah.

2018
May
09

11:00am to 1:00pm

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

11:00am to 1:00pm

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

11:00am to 1:00pm

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

4:00pm to 6:00pm

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

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

2017
May
29

2:00pm to 4:00pm

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

11:00am to 1:00pm

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

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

11:00am to 1:00pm

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

4:00pm to 6:00pm

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.

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.

2015
Nov
11

Repeats every week every Wednesday until Tue Mar 28 2017 except Wed Nov 11 2015.

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Ross 70

Reflections on the coloring and chromatic numbers

Speaker: Chris Lambie-Hanson

Abstract: Compactness phenomena play a central role in modern set theory, and

the investigation of compactness and incompactness for the coloring and chromatic

numbers of graphs has been a thriving area of research since the mid-20th century,

when De Bruijn and Erdős published their compactness theorem for finite chromatic

Speaker: Chris Lambie-Hanson

Abstract: Compactness phenomena play a central role in modern set theory, and

the investigation of compactness and incompactness for the coloring and chromatic

numbers of graphs has been a thriving area of research since the mid-20th century,

when De Bruijn and Erdős published their compactness theorem for finite chromatic

2018
Jan
24

11:00am to 1:00pm

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

11:00am to 1:00pm

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.

This is a joint work with Saharon Shelah.

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