The focus of this project is research in set theory, a subfield of mathematical logic. In set theory we
consider ¿cardinalities¿, which measure the size of infinite sets. We are in particular interested in the
set of all real numbers, and in subsets of this set. Many questions about properties of these sets (e.g. in
connection with the Lebesgue measure) cannot be answered with the usual set-theoretic axioms. The
method of forcing allows us to construct set-theoretic universes in which these answers can be ¿
depending on what you want ¿ yes or no.
In this project we try to further develop the method of forcing. On the one hand, to construct new settheoretic
universes, and on the other hand, in order to better understand the basic properties of the set of
real numbers and its subsets.