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Dr. Yurii Khomskii Amsterdam University College Room 2.27 Science Park 113 1098 XG Amsterdam The Netherlands E-Mail: yurii@deds.nl Lecturer and Academic Tutor               Universität Hamburg Room 409 Fachbereich Mathematik Bundesstraße 55 (Geomatikum) 20146 Hamburg Germany Privatdozent           Institute of Logic, Language and Computation Universiteit van Amsterdam SP107 F1.22C Science Park 107 1098 XG Amsterdam The Netherlands   Guest researcher

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I am a lecturer, academic tutor and researcher in mathematical logic. My main affiliation is

• Lecturer and Academic Tutor at Amsterdam University College.

In addition, I am affiliated as:

• Privatdozent at Hamburg University, in the Mathematical Logic group headed by Prof. Benedikt Löwe


• Guest researcher at the ILLC, University of Amsterdam.

My research interests are in mathematical logic and set theory, specifically the structure of the real line, regularity properties of sets of reals, descriptive set theory and forcing, as well as the generalized real numbers and generalized Baire spaces. I obtained my PhD at the University of Amsterdam in 2012, under the supervision of Prof. Benedikt Löwe and Prof. Jörg Brendle. I obtained my Habilitation at Hamburg University in 2018. Previously, I was a postdoctoral researcher at the Kurt Gödel Research Center for Mathematical Logic at the University of Vienna, a postdoctoral researcher at Hamburg University, and a Marie Sklodowska-Curie research fellow at Hamburg University.

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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, Volume 228, 1 September 2017, pp 208-221.
15. Definable maximal independent families, with Vera Fischer and Jörg Brendle, Proceedings AMS, Volume 147: 8 (2019) pp 3547-3557
16. Bounded Symbiosis and Upwards Reflection, with Lorenzo Galeotti and Jouko Väänänen, submitted (arXiv:2007.14718 [math.LO]).
17. Laver trees in the generalized Baire space, with Marlene Koelbing, Giorgio Laguzzi and Wolfgang Wohofsky, Israel Journal of Mathematics, 2022. doi.org/10.1007/s11856-022-2465-5.
18. Paraconsistent and Paracomplete Zermelo-Fraenkel Set Theory, with Hrafn Oddsson, submitted (arXiv:2210.00057 [math.LO]).

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 materials

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Teaching

At the Amsterdam University College, I teach or have taught the following courses:

• Linear Algebra
• Logic, Information, Argumentation
• Calculus
• Statistics for Sciences
• Mathematical Logic
• Calculus for Economics

In addition, I guide intensive student seminars at Hamburg University on various topics in mathematics, and regularly teach group and individual projects in advanced Set Theory at the ILLC.

Links to recent courses and projects:

• 2023
  • Proseminar "Aussagenlogik und Boolesche Algebren, Hamburg University.
  • Forcing and Independence Proofs, Coordinated January project, ILLC.
• 2022
  • Seminar "Infinite Computability", Hamburg Univesity.
  • Transfinite Computability. Coordinated June project, ILLC.
  • Seminar zu grossen Kardinalzahlen, Hamburg University.
• 2021
  • Seminar "Deskriptive Mengenlehre", Hamburg University.
  • Infinite Games and the Axiom of Determinacy, Coordinated individual project, ILLC.
  • Forcing and Independence Proofs, Coordinated January project, ILLC.
  • Proseminar "Aussagenlogik und Boolsche Algebren", Hamburg University.

Past Teaching

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Latest update: 15.02.2023