Miguel Moreno

Postdoctoral fellow, Department of Mathematics, Bar-Ilan University.


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.



  • 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.


  • 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

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

Spare Time

Some Links

  • Questions on generalised Baire spaces [Link]
  • Bogota Logic Group [Link]
  • Helsinki Logic Group [Link]
  • European Set Theory Society [Link]
  • Set Theory Talks [Link]

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 .