Uniform Roe coronas

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