Talks and Presentations
Invited Talks

28IT.
The Borel reducibility Main Gap

February 2024. 7th workshop on generalised Baire spaces. Invited main speaker. Bristol, England.
Slides

Conference

27IT.
Borelreducibility counterparts of Shelah's classification theory

October 2023. Model Theory Seminar, National University of Colombia. Bogota, Colombia. Online.
Slides

Seminar

26IT.
A Borelreducibility Main Gap

September 2023. Workshop on Generalized Descriptive Set Theory  Annual Meeting of the Swiss Society for Logic and Philosophy of Science. Invited main speaker. Lausanne, Switzerland.
Slides

Conference

25IT.
Classification Theory in Generalized Descriptive Set Theory

September 2023. ÖMG Tagung 2023  Meeting of the Austrian Mathematical Society. Invited special session. Graz, Austria.
Slides

Conference

24IT.
Shelah's Main Gap and the generalized Borelreducibility

July 2023. Sixth workshop on generalised Baire spaces. Vienna, Austria.
Slides

Conference

23IT.
An application of combinatorics into music [ESP]

April 2023. DiscreMath Seminar, National University of Colombia. Bogota, Colombia. Online.
Slides
/
Sounds

Seminar

22IT.
About Filter Reflection

February 2023. Arctic Set Theory Workshop VI. Kilpisjärvi, Finland.
Slides

Conference

21IT.
Finding the main gap in the generalized descriptive set theory

December 2022. Canadian Mathematical Society Winter Meeting. Invited special session. Toronto, Canada.
Slides

Conference

20IT.
Indestructibility and characterization of filter reflection

September 2022. University of Helsinki Logic Seminar. Helsinki, Finland. Online.
Slides

Seminar

19IT.
Reflection of stationary sets and GDST

August 2022. Young Set Theory Workshop 2022. Invited postdoctoral speaker. Novi Sad, Serbia.
Slides

Conference

18IT.
The isomorphism relation of unsuperstable theories in the generalized Borelreducibility

April 26th, 2022. KGRC Set Theory Research Seminar. Vienna, Austria.
Seminar

17IT.
How complex are mathematical theories? [ESP]

March 2022. Internnational Day of Mathematics 2022. Bogota, Colombia.
Slides

Event

16IT.
Kcolorable linear orders and unsuperstable theories

February 2022. Helsinki Logic Seminar  Minisymposium. Helsinki, Finland.
Slides

Minisymposium

15IT.
On unsuperstable theories in the GDST

February 2022. Arctic Set Theory Workshop V. Kilpisjärvi, Finland.
Slides

Conference

14IT.
Colouring orders and ordering trees

February 2022. BarIlan Set Theory Colloquium. Ramat Gan, Israel. Online.
Slides

Seminar

13IT.
Filter Reflection and Generalised Descriptive Set Theory

October 2020. University of Helsinki Logic Seminar. Helsinki, Finland. Online.
Slides

Seminar

12IT.
Filter Reflection

May 2020. BarIlan University and Hebrew University Logic Seminar. Ramat Gan  Jerusalem, Israel. Online.
Slides

Video

Seminar

11IT.
Consistency of Filter Reflection

May 2020. Seminario Flotante de Bogotá de Lógica Matemática. Bogotá Logic Group, Colombia. Online.
Slides

Video

Seminar

10IT.
Connections between generalised Baire spaces and model theory

February 2020. Fifth Workshop on Generalised Baire Spaces. Invited main speaker. Bristol, England.
Slides

Conference

9IT.
Diamond sharp and a model theory dichotomy in GDST

January 2019. Arctic Set Theory Workshop IV. Kilpisjärvi, Finland.
Slides

Conference

8IT.
A model theory dichotomy in generalized descriptive set theory

October 2018. UHCAS Workshop on mathematical logic. Helsinki, Finland.
Slides

Conference

7IT.
La relación de equivalencia modulo conjuntos no estacionarios en los espacios de Baire generalizados

September 2017. Bogotá Logic Seminar. Bogotá, Colombia.
Notes (section 3)

Seminar

6IT.
Conjuntos de indiscernibles en teorias estables

September 2017. Seminario de categorias accessibles y teoria de modelos, Universidad Nacional de Colombia sede Bogotá. Bogotá, Colombia.

5IT.
The equivalence modulo nonstationary ideals

January 2017. Arctic Set Theory Workshop III. Kilpisjärvi, Finland.
Slides

Conference

4IT.
Strong DOP and the Borel hierarchy

September 2016. Workshop on Settheoretical aspects of the model theory of strong logics. Bellaterra, Barcelona.
Slides

Conference

3IT.
Shelah's Main Gap Theorem in the Borelreducibility hierarchy

March 2016. 27th Nordic Congress of Mathematicians. Invited special session. Stockholm, Sweden.
Slides

Conference

2IT.
Borel reducibility and the isomorphism relation

January 2016. Finnish Mathematical Days 2016. Invited special session. Turku, Finland.
Slides

Conference

1IT.
On the reducibility of isomorphism relation

January 2015. Arctic Set Theory Workshop II. Kilpisjärvi, Finland.
Conference
Public Examination

FINDING THE MAIN GAP IN THE BORELREDUCIBILITY HIERARCHY

December 2017. Exactum, Faculty of Science, University of Helsinki.
PDF

Slides

Opponent's lecture
Posters Presentations

2PP.
Filter Reflection and the Borel reducibility

July 2022. Advances in Set Theory 2O22. Jerusalem, Israel.
Poster

Conference

DOI:
10.13140/RG.2.2.16183.60326

1PP.
Filter Reflection and the Borel reducibility

July 2022. ESI Set Theory Workshop 2022. Vienna, Austria.
Poster

Conference

DOI:
10.13140/RG.2.2.16183.60326
Contributed Talks

4CT.
Ordered trees and the kappaBorel reducibility of unsuperstable theories

August  September 2022. European Set Theory Conference 2022. Turin, Italy.
Slides

Video

Conference

3CT.
Diamond sharp and the Generalized Baire Spaces

July 2019. 7th European Set Theory Conference. Vienna, Austria.
Slides

Conf

2CT.
Reflection principles and the generalized Baire spaces

July 2017. 6th European Set Theory conference. Budapest, Hungary.
Slides

Conf

1CT.
The equivalence Modulo Nonstationary Ideals and Shelah's Main Gap Theorem in the Borelreducibility hierarchy

September 2016. Bonn Set Theory Workshop 2016, Generalized Baire spaces. Bonn, Germany.
Slides

Conf
Seminar Talks

25ST.
On the Borel reducibility Main Gap (the weak isolated linear order)

24.01.2024. Logic Seminar, University of Helsinki.

Abstract.
One of the biggest motivations in Generalized Descriptive Set Theory has been the program of identifying counterparts of classification theory in the setting of Borel reducibility. The most important has been the division line classifiable vs nonclassifiable, i.e. identify Shelah's Main Gap in the Borel reducibility hierarchy. This was studied by Friedman, Hyttinen and Weinstein (ne Kulikov) in their book "Generalized descriptive set theory and classification theory". Their work led them to conjecture the following:
If T is a classifiable theory and T' is a nonclassifiable theory, then the isomorphism relation of T is Borel reducible to the isomorphism relation of T'.
In this talk we will prove this conjecture, discuss the objects introduced, and provide a detailed overview of the gaps between classifiable shallow theories, classifiable nonshallow theories, and nonclassifiable theories. The main result that will be presented is the following:
Suppose \kappa=\lambda^+=2^\lambda, 2^c \leq \lambda = \lambda^{\omega_1} and T_1 and T_2 are countable complete firstorder theories in a countable vocabulary.
If T_1 is a classifiable theory and T_2 is a nonclassifiable theory, then the isomorphism relation of T_1 is continuously reducible to the isomorphism relation of T_2, and the isomorphism relation of T_2 is strictly above the isomorphism relation of T_1 in the Borel reducibility hierarchy.
This talk will be based on the article Shelah's Main Gap and the generalized Borelreducibility (https://arxiv.org/abs/2308.07510)
Slides

24ST.
On the Borel reducibility Main Gap (the shallow  nonshallow gap)

17.01.2024. Logic Seminar, University of Helsinki.

Abstract.
One of the biggest motivations in Generalized Descriptive Set Theory has been the program of identifying counterparts of classification theory in the setting of Borel reducibility. The most important has been the division line classifiable vs nonclassifiable, i.e. identify Shelah's Main Gap in the Borel reducibility hierarchy. This was studied by Friedman, Hyttinen and Weinstein (ne Kulikov) in their book "Generalized descriptive set theory and classification theory". Their work led them to conjecture the following:
If T is a classifiable theory and T' is a nonclassifiable theory, then the isomorphism relation of T is Borel reducible to the isomorphism relation of T'.
In this talk we will prove this conjecture, discuss the objects introduced, and provide a detailed overview of the gaps between classifiable shallow theories, classifiable nonshallow theories, and nonclassifiable theories. The main result that will be presented is the following:
Suppose \kappa=\lambda^+=2^\lambda, 2^c \leq \lambda = \lambda^{\omega_1} and T_1 and T_2 are countable complete firstorder theories in a countable vocabulary.
If T_1 is a classifiable theory and T_2 is a nonclassifiable theory, then the isomorphism relation of T_1 is continuously reducible to the isomorphism relation of T_2, and the isomorphism relation of T_2 is strictly above the isomorphism relation of T_1 in the Borel reducibility hierarchy.
This talk will be based on the article Shelah's Main Gap and the generalized Borelreducibility (https://arxiv.org/abs/2308.07510)
Slides

23ST.
Isolation notions and construction of models (SDOP and the construction of models)

17.05.2023. KGRC Model Theory Research Seminar, University of Vienna.

Abstract.
During this talk we introduce the notions of Fconstructible sets and Fprimary models. We use the Fprimary models to show that the isomorphism relation of any classifiable theory T is continuously reducible to the isomorphism relation of any nonclassifiable theory with SDOP.
Notes

22ST.
Isolation notions and construction of models (example and strong types)

10.05.2023. KGRC Model Theory Research Seminar, University of Vienna.

Abstract.
During this talk we give three examples of isolation notions (Ft, Fs, Fa). We introduce the concept of strong type and discuss some of its properties.
Notes

21ST.
Isolation notions and construction of models (motivation and axioms)

3.05.2023. KGRC Model Theory Research Seminar, University of Vienna.

Abstract.
During this talk we will introduce the axioms of isolation notions. We discuss the motivation comming from GDST into the construction of Fpimary models.
Notes

20ST.
Generalised Descriptive Set Theory, part III

28.03.2023. KGRC Set Theory Research Seminar, University of Vienna.

Abstract.
Following part I and part II in this three part series, during this talk we will discuss where in the generalized Borelreducibility hierarchy are the isomorphism relation of first order complete theories. These theories are divided into two kinds: classifiable and nonclassifiable. To study the classifiable theories case is needed the use of EhrenfeuchtFraïssé games. On the other hand the study of the nonclassifiable theories is done by using colored ordered trees. The goal of the talk is to see the classifiable theories case and sketch the ideas of nonclassifiable theories.
Notes

19ST.
Generalised Descriptive Set Theory, part II

21.03.2023. KGRC Set Theory Research Seminar, University of Vienna.

Abstract.
We have introduced the notions of κBorel class, κanalytic class, κanalyticcoanalytic class, κBorel* class in the previous talk. In descriptive set theory the Borel class, the analyticcoanalytic class, and the Borel* class are the same class, we showed that this doesn't hold in the generalized descriptive set theory.
In this talk, we will show the consistency of "κBorel* class is equal to the κanalytic class". This was initially proved by Hyttinen and Weinstein (former Kulikov), under the assumption V=L. We will show a different proof that shows that this holds in L but also can be forced by a cofinalitypreserving GCHpreserving forcing from a model of GCH, but also by a <κclosed κ+‑cc forcing.
Notes

18ST.
Generalised Descriptive Set Theory, part I

14.03.2023. KGRC Set Theory Research Seminar, University of Vienna.

Abstract.
This is the first of three talks about Generalised Descriptive Set Theory. The aim of this talk is to introduce the notions of κ‑Borel class, κ‑analytic class, κ‑analyticcoanalytic class, κ‑Borel* class, and show the relation between these classes.
Notes

17ST.
Fake Reflection

23.01.2020. KGRC Research Seminar, Kurt Gödel Research Center, University of Vienna.

Abstract.
Motivated from many results in generalized descriptive set theory, Filter Reflection (aka Fake Reflection) is an abstract version of reflection compatible with large cardinals, forcing axioms, but also V=L.
In this talk we will present the motivation and definition of filter reflection, we will explain how to force filter reflection and how to force its failure. We will also show some applications and properties of filter reflection, e.g. the consistency of “E^K_{w_1} filter reflects to a subset of E^K_{w}”.
This is a joint work with Gabriel Fernandes and Assaf Rinot.

16ST.
The Main Gap in the generalized Borelreducibility hierarchy

11.03.2019. Set Theory Colloquium, BarIlan University.

Abstract.
During this talk we will discuss where in the generalized Borelreducibility hierarchy are the isomorphism relation of first order complete theories. These theories are divided in two kind:classifiable and nonclassifiable. To study the classifiable theories case is needed the use of EhrenfeuchtFraïssé games. On the other hand the study of the nonclassifiable theories is done by using colored trees. The goal of the talk is to see the classifiable theories case and start the nonclassifiable theories case by proving that it is possible to map every element of the generalized Baire, f, into a colored tree, J(f), such that; for every f and g elements of the generalized Baire space, J(f) and J(g) are isomorphic as colored trees if and only if f and g coincide on a club.

15ST.
An introduction to generalized descriptive set theory, part 4

14.01.2019. Set Theory Colloquium, BarIlan University.

Abstract.
Last week, we gave a detailed proof of Lemma 1.13 from the notes:
http://u.math.biu.ac.il/~morenom3/GDST2018.pdf
This week, we shall continue, proving that, if V=L, then $\kappa$Borel* class is equal to the Sigma1^_1(K) class.

14ST.
An introduction to generalized descriptive set theory, part 3

07.01.2019. Set Theory Colloquium, BarIlan University.

Abstract.
After introducing the notions of KBorel class, KDelta_1^1 class, KBorel^* class we saw some subset relations between them in the previous talk ( http://u.math.biu.ac.il/~morenom3/GDST2018.pdf ). We finished the previous talk with a sketch of the proof of:
if V=L, then $\kappa$Borel* class is equal to the $\Sigma1^ 1(\kappa)$ class.
We will see this proof in complete detail, starting from the key lemma, Lemma 1.13 on the notes.

13ST.
An introduction to generalized descriptive set theory, part 2

31.12.2019. Set Theory Colloquium, BarIlan University.

Abstract.
After introducing the notions of KBorel class, KDelta_1^1 class, KBorel^* class in the previous talk ( http://u.math.biu.ac.il/~morenom3/GDST2018.pdf ), in this talk, we will show the relation between this classes.
In descriptive set theory the Borel class, the Delta_1^1 class, the Borel* class are the same class, this doesn't hold in the generalized descriptive set theory, in particular under the assumption V=L the Borel* class is equal to the Sigma1^_1 class.

12ST.
An introduction to generalized descriptive set theory, part 1

10.12.2018. Set Theory Colloquium, BarIlan University.

Abstract.
This is the first of many of talks in which an overview of the Borelreducibility hierarchy in the generalized Baire space will be given. The aim of this talk is to introduce the notions of KBorel class, KDelta_1^1 class, KBorel^* class, and show the relation between these classes.

11ST.
Σ_1^1complete quasiorders in L

21.03.2018. Logic Seminar, Helsinki Logic Group.

Abstract.
One of the basic differences between descriptive set theory (DST) and generalized descriptive set theory (GDST) is the existence of some analytic sets in GDST that have no counterpart in DST. The equivalence modulo the nonstationary ideal restricted to a stationary set S (EMS) is an example of these sets.
These relations have been studied in GDST to understand some of the differences between DST and GDST. In particular, EMS, with S the set of ordinals with cofinality alpha, has been used to study the isomorphism relations in the Borelreducibility hierarchy. One of the main results related to this is:
If V=L, then EMS, with the set of ordinals with cofinality alpha, is a complete analytic equivalence relation in the generalized Baire space.
From this, it was possible to prove that the isomorphism relation of theories with OCP or SDOP are complete analytic equivalence relations in L(under some cardinal assumptions).
In this talk I will show that the inclusion modulo the nonstationary ideal restricted to the set of ordinals with cofinality alphais is a complete analytic quasiorder in L. This result has many corollary, two of which are:
(V=L) The isomorphism relation of a theory is either a complete analytic equivalence relation or a Delta_1^1 equivalence relation (under some cardinal assumptions).
(V=L) If kappa is not the successor of an omegacofinal cardinal, then the embedability of dense linear orders is a complete analytic relation.

10ST.
Σ_1^1complete quasiorders on weakly compact cardinals

18.10.2017. Logic Seminar, Helsinki Logic Group.

Abstract.
In this talk we prove Σ_1^1complete properties of some quasiorders when K is a weakly compact cardinals.

9ST.
Reflection principles and Borel reducibility

29.03.2017. Logic Seminar, Helsinki Logic Group.

Abstract.
In this talk we explore implications of reflection principles in the Borelreducibility hierarchy.

8ST.
The isomorphism relation of Theories with SDOP

14.09.2016. Logic Seminar, Helsinki Logic Group.

Abstract.
In this talk we explore the Borelreducibility of the isomorphism relation of superstable theories with SDOP.

7ST.
A Borelreducibility counterpart of Shelah's main gap theorem

02.12.2015. Logic Seminar, Helsinki Logic Group.

Abstract.
In this talk we prove a Borelreducibility counterpart of Shelah's main gap theorem.

6ST.
The isomorphism relation of classifable theories

04.11.2015. Logic Seminar, Helsinki Logic Group.

Abstract.
In this talk we explore the Borelreducibility of the isomorphism relation of classifiable theories.

5ST.
On the reducibility of the isomorphism relation II

28.01.2015. Logic Seminar, Helsinki Logic Group.

Abstract.
In this talk we continue exploring the Borelreducibility of the isomorphism relation of stable unsuperstable theories.

4ST.
On the reducibility of the isomorphism relation I

21.01.2015. Logic Seminar, Helsinki Logic Group.

Abstract.
In this talk we explore the Borelreducibility of the isomorphism relation of stable unsuperstable theories.

3ST.
More on Stationary tower forcing

02.03.2014. Logic Seminar, Helsinki Logic Group.

Abstract.
In this talk we continue exploring the definitions and implications of the stationary tower forcing.

2ST.
Stationary tower forcing

22.01.2014. Logic Seminar, Helsinki Logic Group.

Abstract.
In this talk we explore the definitions and implications of the stationary tower forcing.

1ST.
Matroides representables en GF(2)

21.04.2010. Seminario de Estudiantes, Universidad Nacional de Colombia sede Bogotá.

Abstract.
Esta charla tiene como objetivo el dar a conocer algunos métodos para representar matroides en campos ﬁnitos. Para ellos se darán a conocer las nociones básicas de la teoría de matroides y a teoremas básicos de representación de una matroide.