Main research area is the application of set-theoretic techniques, especially infinite combinatorics. A central problem is the existence of universal elements in various classes of models. This problem is sensitive to the underlying set theory, and many times leads to independence results, but still there are results obtained in ZFC (the accepted axiom system for set theory) which concern the class of infinite abelian groups, the class of linear orderings, the class of infinite homogeneous bipartite graphs and other classes

Kojman, M. and Shelah, S., "Universal Abelian Groups," to appear in Israel Journal of Math.

Goldstern, M., Grossberg, R. and Kojman, M., "Infinite Homogeneous Biparatite Graphs With Unequal Sides," to appear in Discrete Mathematics.

Kojman, M. and Shelah, S., "Homogeneous Families and Their Automorphism Groups," to appear in Journal of the London Mathematical Soc.

Goldstern, M. and Kojman, M., "There is No Countable Universal Bridge Free Graph," in preparation.