Research Interests

Publications in Journals

Submitted/In preparation:


• Unbounded version of Zarankiewicz's problem, with A. Papadopoulos, in preparation.
• Orthogonality and domination monoids in o-minimal expansions of ordered groups, with R. Mennuni, in preparation.
• Exact VC-Dimensions of certain geometric set systems, with A. Papadopoulos and F. Westhead, in preparation.
• Definable fields in dense pairs of o-minimal structures, with E. Kaplan and F. Point, in preparation.

Published/Accepted:


• Orthogonal decomposition of definable groups, with A. Berarducci and M. Mamino,
  Journal of Symbolic Logic, to appear, 23 pages.


• On semibounded expansions of ordered groups, with A. Savatovsky,
  Bulletin of the Polish Academy of Sciences - Mathematics , to appear, 15 pages.


• Product cones in dense pairs.
  Mathematical Logic Quarterly, 68 (2022), 279-287.


• Pillay's conjecture for groups definable in weakly o-minimal non-valuational structures,
  Bulletin of the London Mathematical Society, 53 (2021), 1205-1219.


• Strongly minimal groups in o-minimal structures, with A. Hasson and Y. Peterzil,
  Journal of the European Mathematical Society 23 (2021), 3351-3418.


• Counting algebraic points in expansions of o-minimal structures by a dense set,
  Quarterly Journal of Mathematics, 72 (2021), 817-833.


• On coincidence of dimensions in closed ordered differential fields, with O. Leon Sanchez and N. Regnault,
  Notre Dame Journal of Formal Logic, to appear, 12 pages.


• Small sets in Mann pairs,
  Archive for Mathematical Logic, Volume 60 (2021), 317-327.


• Structure theorems in tame expansions of o-minimal structures by a dense set, with A. Günaydin and P. Hieronymi,
  Israel Journal of Mathematics, Volume 239 (2020), 435-500.


• Expansions of real closed fields which introduce no new smooth functions, with A. Savatovsky,
  Annals of Pure and Applied Logic, Volume 171 (2020) 102808, 1-15.


• Locally definable subgroups of semialgebraic groups, with E. Baro and Y. Peterzil,
  Journal of Mathematical Logic, Volume 20 (2020), 2050009, 17 pages.


• The Choice Property in tame expansions of o-minimal structures, with A. Günaydin and P. Hieronymi,
  Mathematical Logic Quarterly, Volume 66 (2020), 239-246.


• Characterizing o-minimal groups in tame expansions of o-minimal structures (previously titled "Large groups are o-minimal".)
  Journal of the Institute of Mathematics of Jussieu, Online first (2019), 26 pages.


• Small sets in dense pairs,
  Israel Journal of Mathematics 233 (2019), 1-27 pages.


• Semi-linear stars are contractible,
  Fundamenta Mathematicae, Volume 241 (2018), 291-312.


• On definable Skolem functions in weakly o-minimal non-valuational structures, with A. Hasson and G. Keren,
  Journal of Symbolic Logic, Volume 82 (2017), 1482-1495.


• Interpretable groups are definable, with Y. Peterzil and J. Ramakrishnan,
  Journal of Mathematical Logic, Volume 14, No. 1 (2014), 47 pages.


• Coverings by open cells, with M. Edmundo and L. Prelli,
  Archive for Mathematical Logic, Volume 53 (2014), 307-325.


• The universal covering map in o-minimal expansions of groups, with M. Edmundo and L. Prelli,
  Topology and its Applications, Volume 160 (2013), 1530-1556.


• Lattices in locally definable subgroups of (R^n, +), with Y. Peterzil,
  Notre Dame Journal of Formal Logic, Volume 54, Number 3-4 (2013), 449-461.


• Non-standard lattices and o-minimal groups,
  Bulletin of Symbolic Logic, Volume 19 (2013), 56-76.


• Definable groups as homomorphic images of semilinear and field-definable groups, with Y. Peterzil,
  (Correction)
  Selecta Mathematica N.S., Volume 18 (2012), 905-940.


• Definable quotients of locally definable groups, with Y. Peterzil,
  Selecta Mathematica N.S., Volume 18 (2012), 885-903.


• Local analysis for semi-bounded groups,
  (Corollary 4.4 has been amended -- the published statement was wrong and unused)
  Fundamenta Mathematicae, Volume 216 (2012), 223-258.


• Notions of bisimulation for Heyting-valued modal languages, with C. Koutras and C. Nomikos,
  Journal of Logic and Computation, Volume 22 (2012), 213-235.


• Groups definable in linear o-minimal structures: the non-compact case,
  Journal of Symbolic Logic, Volume 75 (2010), 208-220.


• Compact domination for groups definable in linear o-minimal structures,
  Archive for Mathematical Logic, Volume 48, Issue 7 (2009), 607-623.


• Definable group extensions in semi-bounded o-minimal structures, with M. Edmundo,
  Mathematical Logic Quarterly, Volume 55 (2009), 598-604.


• A semi-linear group which is not affine,
  Annals of Pure and Applied Logic 156 (2008), 287-289.


• The universal covering homomorphism in o-minimal expansions of groups, with M. Edmundo,
  Mathematical Logic Quarterly, Volume 53 (2007), 571-582.


• Groups definable in ordered vector spaces over ordered division rings, with S. Starchenko,
  Journal of Symbolic Logic, Volume 72 (2007), 1108-1140.


• Frame constructions, truth invariance and validity preservation in many-valued modal logic, with C. Koutras,
  Journal of Applied Non-Classical Logics, Volume 15 - No. 4 (2005), 367-388.

Publications in Conference Proceedings (refereed/non-refereed)

• From Logic to Geometry,
  Symposium for 90 years of Mathematics, Aristotle University of Thessaloniki (to appear).


• Counting algebraic points in expansions of o-minimal structures by a dense set,
  Séminaire de structures algébriques ordonnées, F. Delon, M. Dickmann, D. Gondard, T. Servi (eds), Paris 6 - 7, Equipe de Logique Mathématique Prépublications, (2017-2018).


• Small sets in dense pairs,
  Oberwolfach Reports 22 (2017).


• On weakly o-minimal non-valuational structures, with A. Hasson and G. Keren,
  Proceedings of 10th Panhellenic Logic Symposium, Samos (2015).


• Semi-bounded groups,
  Proceedings of 9th Panhellenic Logic Symposium, Athens (2013).


• Notions of Bisimulation for Heyting-Valued Modal Languages, with C. Koutras and C. Nomikos,
  Proceedings of Computability in Europe 2008 (CiE 2008), A. Beckman, C. Dimitracopoulos, B. Loewe (eds), Logic and Theory of Algorithms, Athens University Press (2008), pp. 117-126.

Habilitation

• Structure theorems and applications in semi-bounded and tame pairs, University of Konstanz, May 2018.

Ph.D. Thesis

• Groups definable in linear o-minimal structures, University of Notre Dame, July 2007.

Notes

• Pregeometries and imaginaries, May 2005.

Notes from seminar talks

• Groups definable in o-minimal structures.
• The descending chain condition for o-minimal groups.