I am a postdoctoral fellow at the Department of Mathematics, Bar-Ilan University, under the supervision of Prof. Assaf Rinot.

**News**: The Finnish Adacemy of Science and Letters (Suomalainen Tiedeakatemia) has awarded me with a grant for my post-doctoral project **"The Borel-reducibility hierarchy and generalized descriptive set theory"**. The grant awarded from Saatioiden post doc -pooli is intended to conduct the research abroad from Finland.

**Erdös number**: 3

**Research interests**:

**Model theory**: Classification theory, stability theory.

**Set theory**: Generalized descriptive set theory (GDST), tower forcing, generic absolutness, large cardinals.

**Publications**

- Tapani Hyttinen, Vadim Kulikov, Miguel Moreno,
*A generalized Borel-reducibility counterpart of Shelah’s main gap theorem*. Arch. Math. Logic (2017) 56: 175 – 185. [PDF] - Tapani Hyttinen, Miguel Moreno,
*On the Reducibility of Isomorphism Relations*. Mathematical Logic Quarterly (2017) 63: 175 – 192.[PDF] - Miguel Moreno,
*The isomorphism relation of theories with S-DOP in generalized Baire spaces*. Submitted. [arXiv] - Tapani Hyttinen, Vadim Kulikov, Miguel Moreno,
*On \Sigma_1^1-completeness of Quasi-orders on \kappa^\kappa*. Submitted. [arXiv]

**Working Papers and Projects**

*Inclusion modulo nonstationary*with Gabriel Fernandes and Assaf Rinot.*On Unsuperstable Theories in GDST.*

**Theses**

- Miguel Moreno,
*FINDING THE MAIN GAP IN THE BOREL-REDUCIBILITY HIERARCHY*, University of Helsinki, faculty of Science, Department of Mathematics and Statistics; Doctoral dissertation (article-based), advisor Tapani Hyttinen. Unigrafia, Helsinki (2017).[PDF] [public examination] - Miguel Moreno,
*The stationary tower forcing*, University of Bonn; Master thesis, advisor Peter Koepke (co-advise by Philipp Schlicht). Bonn (2013). - Miguel Moreno,
*Matroides Representables*, National University of Colombia, Bogota; Bachelor thesis, advisor Humberto sarria. Bogota (2010).

**Lecture notes**

- Generalized Descriptive Set Theory at Bar-Ilan University (2019, series of lectures)
- Combinatorics at Helsinki University (winter semester 2018, bachelor level course)
- Introduction to Generalized Descriptive Set Theory at Universidad Nacional de Colombia (2017, research visit)

**Selected Talks**

- January 2019.
*Diamond sharp and a model theory dichotomy in GDST*. Arctic Set Theory Workshop IV. [Slides] - October 2018.
*A model theory dichotomy in generalized descriptive set theory*. UH-CAS Workshop on mathematical logic. [Slides] - July 2017.
*Reflection principles and the generalized Baire spaces*. 6th European Set Theory conference. [Slides] - January 2017.
*The equivalence modulo non-stationary ideals*. Arctic Set Theory Workshop III. [Slides] - September 2016.
*Strong DOP and the Borel hierarchy*. Workshop on Set-theoretical aspects of the model theory of strong logics. [Slides] - September 2016.
*The equivalence Modulo Non-stationary Ideals and Shelah's Main Gap Theorem in the Borel-reducibility hierarchy*. Bonn Set Theory Workshop 2016, Generalized Baire spaces. [Slides] - March 2016.
*Shelah's Main Gap Theorem in the Borel-reducibility hierarchy*. 27th Nordic Congress of Mathematicians. [Slides] - January 2016.
*Borel reducibility and the isomorphism relation*. Finnish Mathematical Days 2016 [Slides]. - January 2015.
*On the reducibility of isomorphism relation*. Arctic Set Theory Workshop II.

**Forthcoming Events**

- June 2019. Young Set Theory Workshop 2019
- July 2019. 7th European Set Theory Conference

**Spare Time**

- Popular science article, Is it possible that you really don't have choice?
- Two Math Questions

**Some Links**

#### Contact information

Office: Building 216, Room 008

Address: P.O. Box 26, Department of Mathematics, Bar-Ilan University,

Max and Anna Webb street, Ramat-Gan, 5290002, Israel.

Email: morenom3 'at' macs.biu.ac.il

Phone:+972-3-531-7235 .