  In this paper we show that the $\mathrm{K}$-homology groups of a separable
C*-algebra can be enriched with additional descriptive set-theoretic
information, and regarded as definable groups. Using a definable version of the
Universal Coefficient Theorem, we prove that the corresponding definable
$\mathrm{K}$-homology is a finer invariant than the purely algebraic one, even
when restricted to the class of UHF C*-algebras, or to the class of unital
commutative C*-algebras whose spectrum is a $1$-dimensional connected subspace
of $\mathbb{R}^{3}$.
