  Given a link L in the 3-sphere, we ask whether the components of L bound
disjoint, nullhomologous disks properly embedded in a simply-connected
positive-definite smooth 4-manifold; the knot case has been studied extensively
in work of Cochran-Harvey-Horn. Such a 4-manifold is necessarily homeomorphic
to a (punctured) connected sum of CP(2)'s. We characterize all links that are
slice in a (punctured) connected sum of CP(2)'s in terms of ribbon moves and an
operation which we call adding a generalized positive crossing. We find
obstructions in the form of the Levine-Tristram signature function, the signs
of the first author's generalized Sato-Levine invariants, and certain Milnor's
invariants. We show that the signs of coefficients of the Conway polynomial
obstruct a 2-component link from being slice in a single punctured CP(2) and
conjecture these are obstructions in general. These results have applications
to the question of when a 3-manifold bounds a 4-manifold whose intersection
form is that of some connected sum of CP(2)'s. For example, we show that any
homology 3-sphere is cobordant, via a smooth positive definite manifold, to a
connected sum of surgeries on knots in the 3-sphere.
