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Extremely metal-poor (EMP) stars in the Milky Way (MW) allow us to infer theproperties of their progenitors by comparing their chemical composition to themetal yields of the first supernovae. This method is most powerful when appliedto mono-enriched stars, i.e. stars that formed from gas that was enriched byonly one previous supernova. We present a novel diagnostic to identify thissubclass of EMP stars. We model the first generations of star formationsemi-analytically, based on dark matter halo merger trees that yield MW-likehalos at the present day. Radiative and chemical feedback are includedself-consistently and we trace all elements up to zinc. Mono-enriched starsaccount for only $\sim 1\%$ of second generation stars in our fiducial modeland we provide an analytical formula for this probability. We also present anovel analytical diagnostic to identify mono-enriched stars, based on the metalyields of the first supernovae. This new diagnostic allows us to derive ourmain results independently from the specific assumptions made regarding Pop IIIstar formation, and we apply it to a set of observed EMP stars to demonstrateits strengths and limitations. Our results may provide selection criteria forcurrent and future surveys and therefore contribute to a deeper understandingof EMP stars and their progenitors.

Descendants of the first stars: the distinct chemical signature of second generation stars