  In a many-to-one matchingmodel with responsive preferences in which
indifferences are allowed, we study three notions of core, three notions of
stability, and their relationships. We show that (i) the core contains the
stable set, (ii) the strong core coincides with the strongly stable set, and
(iii) the super core coincides with the super stable set. We also show how the
core and the strong core in markets with indifferences relate to the stable
matchings of their associated tie-breaking strict markets.
