UPPSALA UNIVERSITY
Department of Mathematics
Vera Koponen
Research
Theme
I do research in
model theory
in mathematical logic.
Research themes include investigating and classifying
infinite structures that are, in one way or other, limits of finite structures, in particular (ultra)homogeneous structures, or probabilistic limit structures. Often methods from model theoretic classification theory (stability/simplicity theory) are used. Recent articles use methodology for studying limit behaviour of finite structures to problems concerning probabilistic inference within a branch of AI called Statistical Relational Artificial Intelligence (or Statistical Relational Learning).
Publications and preprints
On the relative asymptotic expressivity of inference frameworks,
with Felix Weitkämper
(arXiv).
Asymptotic elimination of partially continuous aggregation functions in
directed graphical models,
with Felix Weitkämper
(arXiv).
Conditional probability logic, lifted Bayesian networks, and almost sure quantifier elimination
(arXiv),
Theoretical Computer Science 848 (2020) 1-27.
Supersimple omega-categorical theories and pregeometries
(arXiv), Annals of Pure and Applied Logic,
Vol 170 (2019).
On constraints and dividing in ternary homogeneous structures
(arXiv), The Journal of Symbolic Logic,
Vol. 83 (2018) 1691-1721.
Binary simple homogeneous structures
(pdf),
Annals of Pure and Applied Logic, Vol. 169 (2018) 1335-1368.
Binary primitive homogeneous simple structures
(pdf), The Journal of Symbolic Logic,
Vol. 82 (2017) 183-207.
Homogeneous 1-based structures and interpretability in random structures
(pdf),
Mathematical Logic Quarterly, Vol. 63 (2017) 6-18.
Random l-colourable structures with a pregeometry,
with Ove Ahlman,
(pdf),
Mathematical Logic Quarterly, Vol. 63 (2017) 32-58.
Binary simple homogeneous structures are supersimple with finite rank
(pdf),
Proceedings of the American Mathematical Society, Vol. 144 (2016) 1745-1759.
On sets with rank one in simple homogeneous structures, with Ove Ahlman
(pdf),
Fundamenta Mathematicae, Vol. 228 (2015) 223-250.
Typical automorphism groups of finite nonrigid structures
(pdf), Archive for Mathematical Logic, Vol. 54 (2015) 571-586.
Limit laws and automorphism groups of random nonrigid structures,
with Ove Ahlman, Journal of Logic and Analysis, Vol. 7:2 (2015) 1-53. Open access online.
On compactness of logics that can express properties of symmetry or connectivity, with Tapani Hyttinen,
(pdf), Studia Logica, Vol. 103 (2015) 1-20.
(online).
A limit law of almost l-partite graphs,
(pdf), The Journal of Symbolic Logic, Vol. 78, (2013) 911-936.
Random graphs with bounded maximum degree: asymptotic
structure and a logical limit law
(open access online),
Discrete Mathematics and Theoretical Computer Science, Vol. 14 (2012) 229-254.
Asymptotic probabilities of extension properties and random l-colourable structures
(pdf), Annals of Pure and Applied Logic, Vol. 163 (2012) 391-438.
(Online.)
Some connections between finite and infinite model theory (pdf), in
Esparza, Michaux and Steinhorn (Eds.),
Finite and Algorithmic Model Theory,
London Mathematical Society Lecture Note Series 379, Cambridge University Press (2011) 109-139.
Independence and the finite submodel property,
Annals of Pure and Applied Logic, Vol. 158 (2009) 58-79 (pdf).
Entropy of formulas, Archive for Mathematical Logic, Vol. 48, No. 6 (2009), 515-522 (pdf).
Review of the book Finite Structures with Few Types, The Bulletin of Symbolic Logic, Vol. 14, No. 1 (March 2008), 114-116.
Finite satisfiability and $\aleph_0$-categorical structures with trivial dependence,
The Journal of Symbolic Logic, Vol. 71, No. 3 (September 2006), 810-830. (pdf)
The finite submodel property and $\omega$-categorical expansions of pregeometries, Annals of Pure and Applied Logic,
Vol. 139 (May 2006), 201-229. (pdf)
A note on orthogonality and stable embeddedness (with G. Cherlin and E. Hrushovski),
The Journal of Symbolic Logic, Vol. 70, No. 4 (December 2005), 1359-1364. (pdf)
On first-order sentences without finite models, The Journal of Symbolic Logic, Vol. 69, No, 2 (June 2004), 329-339.
Note: There is an erroneous step in the proof of Proposition 4 in this article; consequently, Proposition 4 and Theorem 1 are not proved
(so the assertions they make are still open).
Finite variable logic, stability and finite models, The Journal of Symbolic Logic, Vol. 66, No. 2 (June 2001), 837-858.
Stability theory in finite variable logic
(pdf), Ph.D. thesis, Uppsala, 2000.
Remark: In older items of the list, my former name appears.