We show that if a rational homology 3-sphere Y bounds a positive definite smooth 4-manifold, then there are finitely many negative definite lattices, up to the stable-equivalence, which can be realized as the intersection form of a smooth 4-manifold bounded by Y. To this end, we make use of constraints on definite forms bounded by Y induced from Donaldson`s diagonalization theorem, and Ozsvath and Szabo`s Heegaard Floer correction term. We also present some families of Seifert fibered 3-manifolds that bound both positive and negative definite smooth 4-manifolds.