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Dr. Yurii Khomskii Universität Hamburg Fachbereich Mathematik Bereich Mathematische Logik und interdisziplinäre Anwendungen der Logik Bundesstraße 55 (Geomatikum) 20146 Hamburg Room 409 Tel: +49 40 42838-3313 E-Mail: yurii@deds.nl

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I am a Marie Sklodowska-Curie research fellow at the University of Hamburg, in the Mathematical Logic group headed by Prof. Benedikt Löwe.

Prior to that, I was a postdoctoral researcher at the Kurt Gödel Research Center for Mathematical Logic at the University of Vienna, under leadership of Prof. Sy David Friedman. I obtained my PhD at the University of Amsterdam, under the supervision of Benedikt Löwe and Jörg Brendle.

I obtained my Habilitation at the University of Hamburg in April 2018.

My research interests are in mathematical logic and set theory, specifically the structure of the real line, descriptive set theory and forcing.

My complete CV can be found here.

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Publications

Papers

1. A General Setting for the Pointwise Investigation of Determinacy, Proceedings of the Third Indian Conference on Logic and Applications, (Eds.) R. Ramanujam and Sundar Sarukkai, Springer LNAI 5378, 2009, pp 187--197.
2. William of Sherwood, Singular Propositions and the Hexagon of Opposition, Jean-Yves Beziau and Gillman Payette (eds.), New Perspectives on the Square of Opposition, Peter Lang, Bern, 2010.
3. Polarized partitions on the second level of the projective hierarchy, with Jörg Brendle, Annals of Pure and Applied Logic 163, 2012. pp 1345-1357.
4. Mad families constructed from perfect almost disjoint families, with Jörg Brendle, Journal of Symbolic Logic 78:4 , pp. 1164-1180.
5. Co-analytic mad families and projective well-orders, with Vera Fischer and Sy Friedman, Archive for Mathematical Logic 52:7-8, 2013, pp 809-822.
6. Projective Hausdorff gaps, Archive for Mathematical Logic 53:1-2, 2014, pp 57-64.
7. Cichon's diagram, regularity properties and Δ¹₃ sets of reals, with Vera Fischer and Sy Friedman, Archive for Mathematical Logic 53:5-6, 2014, pp 695-729.
8. Measure, category, and projective well-orders, with Vera Fischer and Sy Friedman, Journal of Logic and Analysis 6, Paper 8, 2014 (25 pp)
9. Regularity properties on the generalized reals, with Sy Friedman and Vadim Kulikov, Annals of Pure and Applied Logic 167:4, 2016, pp 408-430
10. Questions on Generalised Baire Spaces, with Giorgio Laguzzi, Benedikt Löwe and Ilya Sharankou, Mathematical Logic Quarterly 62:4-5, August 2016, pp 439-456.
11. Almost disjoint refinements and mixing reals, with Barnabas Farkas and Zoltán Vidnyánszky, Fundamenta Mathematicae 242 (2018), pp 25-48.
12. Full-splitting Miller trees and infinitely often equal reals, with Giorgio Laguzzi, Annals of Pure and Applied Logic 168:8, 2017, pp 1491–1506.
13. Cofinalities of Marczewski ideals, with Jörg Brendle and Wolfgang Wohofsky, Colloquium Mathematicum 150 (2017), pp 269-279.
14. Filter-Laver measurability, Topology and its Applications, to appear.
15. Definable maximal independent families, with Vera Fischer and Jörg Brendle, Proceedings AMS, to appear.
16. Laver trees in the generalized Baire space, with Marlene Koelbing, Giorgio Laguzzi and Wolfgang Wohofsky, in preparation.
17. Symbiosis and Upwards Reflection, with Lorenzo Galeotti and Jouko Väänänen, in preparation.
18. Eventually different trees, in preparation.

Theses

1. Banach Algebras, Bachelor Thesis, Leiden University. (Supervisor: Dr. Marcel de Jeu)
2. Regularity Properties and Determinacy, Master Thesis, University of Amsterdam. (Supervisor: Dr. Benedikt Löwe)
3. Regularity Properties and Definability in the Real Number Continuum, PhD Thesis, University of Amsterdam, 2012. ILLC Dissertation Series DS-2012- 04. (Supervisor: Benedikt Löwe, co-supervisor: Jörg Brendle)
4. Habilitationsschrift: Cardinal Characteristics, Regularity Properties, Definability and the Structure of the Real Line and the Generalised Real Line

Notes and course material

Slides to talks

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Teaching

• January 2019
  • Advanced Topics in Set Theory, January Project, ILLC.
• Fall 2018
  • Vertiefung Mengenlehre, Hamburg University.
• June 2018
  • Advanced Topics in Set Theory, June Project, ILLC.
• January 2018
  • Alternative Set Theories, January project, ILLC, University of Amsterdam
• June 2017
  • Seminars in Set Theory, with Lorenzo Galeotti, June project, ILLC, University of Amsterdam
• Spring 2016
  • Vertiefung Mengenlehre, Hamburg University.
• Fall 2013
  • Set Theory Reading Course, Kurt Gödel Research Center, University of Vienna.
• June 2013
  • Invited lecture series Unbeatable Stragies, at the HIM programme Stochastic Dynamics in Economics and Finance, Bonn, Germany (invitation by Prof. Igor Evstigneev).
• Fall 2011
  • Logic, Information flow and Argumentation, lectureship at Amsterdam University College (AUC).
  • Modal Logic (Bachelor of Mathematics and Master of Logic programme, UvA)
• Spring 2011
  • Set Theory (Mastermath programme)
  • Intuitionistic Logic (Master of Logic programme, UvA)
• Summer 2010
  • Intensive course on Infinite Games, teachers' exchange programme at FMI, Sofia University, Bulgaria.
• Fall 2008
  • Capita Selecta: Set Theory, Model Theory (Master of Logic programme, Master of Mathematics programme, UvA). Together with Benedikt Löwe and Brian Semmes.
• Spring 2008
  • Axiomatic Set Theory (Master of Logic programme, Bachelors of Mathematics programme, UvA)
  • Intuitionistic Logic (Master of Logic programme, UvA)
• Fall 2007
  • Recursion Theory (Master of Logic programme, UvA)

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Organizational activities

• Colloquium Logicum 2016 (biannual DVMLG meeting), Hamburg, Germany.
• Mini-symposium in Set Theory, DMV 2015, Hamburg, Germany.

In the past, I have organized the following academic activites:

• Amsterdam workshop in set theory, 26-27 May, 2009 (satellite workshop to the PhD defense of Brian Semmes)
• In the period 2009-2011, I was co-organizer of the Logic Tea at the University of Amsterdam
• Amsterdam workshop in set theory, 1-2 June, 2010 (satellite workshop to the PhD defense of Daisuke Ikegami)

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Latest update: 28.05.2018