Accessibility and the solution set condition (Q1346709)

It was observed by \textit{M. Makkai} and \textit{R. Paré} [``Accessible categories'', Contemp. Math. 104 (1989; Zbl 0703.03042)] that given accessible categories \({\mathcal K}\) and \({\mathcal L}\), every accessible functor \(F : {\mathcal K} \to {\mathcal L}\) satisfies the solution-set condition. In the present paper the authors prove that, conversely, the solution-set condition guarantees that \(F\) is accessible. This result requires, in fact is equivalent to, the large cardinal Vopenka's principle.