We introduce a stochastic halo formation model to compute the early chemical enrichment of the interstellar medium ( ISM ) of the halo .
Contrary to 1-zone chemical evolution models , we are able to resolve local inhomogeneities in the ISM caused by single core-collapse supernovae .
These inhomogeneities lead to different element abundance patterns in very metal-poor stars , which can be seen as scatter in the abundances of halo stars with metallicities [ Fe/H ] < 2.0 .

The early chemical evolution of the halo proceeds in different enrichment phases : At [ Fe/H ] < -3.0 , the halo ISM is unmixed and dominated by local inhomogeneities caused by individual core-collapse supernova ( SN ) events .
For metallicities [ Fe/H ] > -2.0 the halo ISM is well mixed , showing an element abundance pattern integrated over the initial mass function .
In the range -3.0 < [ Fe/H ] < -2.0 a continuous transition from the unmixed to the well mixed ISM occurs .

For some elements ( Si , Ca , Eu ) , the scatter in the element-to-iron ratio [ El/Fe ] of metal-poor halo stars can be reproduced .
Stellar yields of other elements predict a scatter which , compared to the observations , is too large ( O , Mg ) or too small ( Ni ) .
Cr and Mn show a decreasing trend for lower metallicities , which can not be explained by metallicity independent yields , provided that the mixing of the ejecta with the interstellar medium does not depend on progenitor mass .
This demonstrates the need for revised , self-consistent SN yields .

Finally , we discuss the metallicity distribution in the model .
Compared to the 28 very metal-poor stars observed with metallicities in the range -4.0 < [ Fe/H ] < -3.0 , no star is known with confirmed metallicity [ Fe/H ] < -4.0 , while our model predicts 5 \pm 2 stars with [ Fe/H ] < -4.0 .
These should be present if the halo ISM started at primordial metallicities and no pre-enrichment by population III stars occurred .