The Uses of Set Theory The Mathematical Intelligencer, Vol. 14,
No. 1 (1992), 63-69. In this article Roitman gives six examples
from analysis, algebra, and algebraic topology whose results
make use of modern set-theoretic techniques. These examples are
The ideal of compact operators The purely analytic question "Is
the ideal of compact operators on Hilbert space the sum of two
properly smaller ideals?" is equivalent to purely set-theoretic
combinatorics. A characterization of free groups The proof that
"an Abelian group is free if and only if it has a discrete norm"
exploits the use of model theory within set theory. The
fundamental group The proof that "the fundamental group of a
nice space is either finitely generated or has cardinality of
the first uncountable cardinal" uses methods related to
consistency results. The Hawaiian Earring Questions in strong
homology theory are related to consistency results and the
continuum hypothesis. A Banach space with few operators An
example of a nonseparable Banach spa