  In the paper we study choice functions on posets satisfying the conditions of
heredity and outcast. For every well-ordered sequence of elements of poset, we
define the corresponding `elementary' choice function. Every such a choice
function satisfies the conditions of heredity and outcast. Inversely, every
choice functions satisfying the conditions of heredity and outcast can be
represented as union of several elementary choice functions. This result
generalizes the Aizerman-Malishevsky theorem about structure of
path-independent choice functions.
