The Hausdorff medal is awarded biennially (i.e. once every two years) for the most influential work in set theory published in the five years preceding the medal.
General topology meets model theory, on p and t. Proc. Natl. Acad. Sci. USA 110 (2013), no. 33, 13300-13305,
and then expounded in the detailed, 60 page long version:
Cofinality spectrum theorems in model theory, set theory, and general topology. J. Amer. Math. Soc. 29 (2016), no. 1, 237-297.
The medal was awarded to the paper
K without the measurable, The Journal of Symbolic Logic, Volume 78, Issue 3 (2013), pp.708-734
by Ronald Jensen and John Steel.
The medal medal was awarded to the papers
Suitable extender models I. J. Math. Log. 10 (2010), no. 1-2, pp.101–339
Suitable extender models II: beyond omega-huge. J. Math. Log. 11 (2011), no. 2, pp.115–436
by W. Hugh Woodin, where the author made a major contribution to the inner model theory of supercompact cardinals and beyond.