Our final chapter is the translation of two papers of Arnould Bayart (1911-1998) with an introduction and commentary on his presentation of a possible-worlds semantics for a predicate logic based on S5, together with a completeness proof. With an introduction and a commentary, they appeared in Cresswell (2015) in Logique et Analyse, an article reproduced here as it appeared there, except for the reformatting necessary for inclusion in this book and a short biographical endnote. In 1958, Arnould Bayart produced a semantics for first- and second-order S5 modal logic, ‘Soundness of S5 modal predicate logic’, and in 1959, a completeness proof for first-order S5 and what he calls a ‘quasi-completeness’ proof for second-order S5, ‘Completeness of S5 modal predicate logic’. The 1959 paper is the first completeness proof for modal predicate logic based on the Henkin construction of maximal consistent sets and indeed may be the earliest application of the Henkin method even to propositional modal logic. The semantics is in terms of possible worlds which Bayart notes can be anything at all.