  Extremely metal-poor (EMP) stars in the Milky Way (MW) allow us to infer the
properties of their progenitors by comparing their chemical composition to the
metal yields of the first supernovae. This method is most powerful when applied
to mono-enriched stars, i.e. stars that formed from gas that was enriched by
only one previous supernova. We present a novel diagnostic to identify this
subclass of EMP stars. We model the first generations of star formation
semi-analytically, based on dark matter halo merger trees that yield MW-like
halos at the present day. Radiative and chemical feedback are included
self-consistently and we trace all elements up to zinc. Mono-enriched stars
account for only $\sim 1\%$ of second generation stars in our fiducial model
and we provide an analytical formula for this probability. We also present a
novel analytical diagnostic to identify mono-enriched stars, based on the metal
yields of the first supernovae. This new diagnostic allows us to derive our
main results independently from the specific assumptions made regarding Pop III
star formation, and we apply it to a set of observed EMP stars to demonstrate
its strengths and limitations. Our results may provide selection criteria for
current and future surveys and therefore contribute to a deeper understanding
of EMP stars and their progenitors.
