The main contribution of this paper is a formal characterization of recursive object specifications based on a denotational untyped semantics of the object calculus and the discussion of existence of those (recursive) specifications. The semantics is then applied to prove soundness of a programming logic [2] for the object calculus [1] and to suggest possible extensions. For the purposes of this discussion we use an informal logic of predomains in order to avoid any commitment to a particular syntax of specification logic.