Kerkko Luosto, Ph.D. in Mathematics, docent

Research Interests

I have been mainly working on abstract and finite model theory, concentrating on quantifier hierarchies, implicit definability, Löwenheim-Skolem numbers and related concepts. As tools, I am interested in Ramsey theory and ultraproducts.

Available Preprints

Equicardinality on linearly ordered structures, Extension of the abstract for Logic Colloquium 2001, Vienna. [ps] [pdf]

(with Ari Koponen ) Definability issues in finite group theory, Reports of the Department of Mathematics, University of Helsinki 227. [ps]

Classifying unary quantifiers, Preprint 496, Department of Mathematics and Statistics, University of Helsinki, 2009, [pdf]

On vectorizations of unary generalized quantifiers, manuscript, 2009, [pdf]

(with Juha Kontinen and Lauri Hella) Regular Representations of Uniform $TC^0$, Preprint 25, Mittag-Leffler institute, autumn 2009, [pdf]

List of Publications

[1] (with Lauri Hella ) The Beth-closure of ${\cal L}(Q_\a)$ is not finitely generated , Journal of Symbolic Logic 57, no. 2 (1992), 442--448

[2] Filters in abstract model theory , Ph.D. Thesis 81 pp., Helsinki 1992.

[3] (with Lauri Hella) Finite generation problem and n-ary quantifiers, in M. Krynicki, M. Mostowski and L. W. Szczerba (eds.): Quantifiers: Logics, Models and Computation, Kluwer Academic Publishers 1995, 63--104.

[4] (with L. Hella and P. Kolaitis ) How to define linear order on finite models, Annals of Pure and Applied Logic 87 (1997), 241--267. A preliminary version appeared in Proceedings of 9th IEEE Symposium on Logic in Computer Science 1994, 40--49.

[5] (with L. Hella and J. Väänänen ) The hierarchy theorem for generalized quantifiers, Journal of Symbolic Logic 61 (1996), 802-819.

[6] Ultrametric spaces bi-Lipschitz embeddable in ${\Bbb R}^n$ , Fundamenta Mathematicae 150 (1996), 25--42.

[7] (with L. Hella and P. Kolaitis) The almost everywhere equivalence of logics, Bulletin of Symbolic Logic 2 (1996), 422--443.

[8] Ramsey theory is needed for solving definability problems of generalized quantifiers, Lecture Notes in Computer Science 1754 (1999), 121--134.

[9]Hierarchies of monadic generalized quantifiers, Journal of Symbolic Logic 65 (2000), 1241-1263.

Contact information

Email is by far the best possible way to contact me from distance: Kerkko.Luosto@Helsinki.Fi. For the normal mail address, telephone and fax numbers, see the departmental catalogue.