The tools of modern combinatorial set theory, such as combinatorial principles, partition calculus, infinite trees, ultrapowers, forcing axioms, and large cardinal axioms, have been very successful in resolving problems in areas such as general topology, abstract functional analysis, measure theory, and algebra.

The topics include (but are not limited to):

1.Logical Foundations of Mathematics
2.Large Cardinal properties
3.Independence and Large Cardinals
4.Consistency of large cardinal axioms
5.Large cardinal axioms and Grothendieck universes
6.Implications between strong large cardinal axioms
7.Solovay hierarchy
8.Large Cardinals with forcing
9.Large Cardinals and Consistency Results in Topology
10.Infinitary languages and classification of uncountable structures
11.Applications of set theory to Banach spaces, algebra, topology and measure theory
12.Inner models of large cardinals and aspects of determinacy
13. Contemporary nonstandard analysis and possible generalizations