  A uniform Roe corona is the quotient of the uniform Roe algebra of a metric
space by the ideal of compact operators. Among other results, we show that it
is consistent with ZFC that isomorphism between uniform Roe coronas implies
coarse equivalence between the underlying spaces, for the class of uniformly
locally finite metric spaces which coarsely embed into a Hilbert space.
Moreover, for uniformly locally finite metric spaces with property A, it is
consistent with ZFC that isomorphism between the uniform Roe coronas is
equivalent to bijective coarse equivalence between some of their cofinite
subsets. We also find locally finite metric spaces such that the isomorphism of
their uniform Roe coronas is independent of ZFC. All set-theoretic
considerations in this paper are relegated to two 'black box' principles.
