  §4.  Concerning the undefinability theorem for L(ω1,ω1). Carol Karp remarks (1964, 166), “At the International Congress of Logic, Methodology and the Philosophy of Science at Stanford University in 1960, Dana Scott circulated an outline of a proof of the impossibility of a complete definable formal system for (γ+, γ+) languages with a single two-place predicate symbol in addition to the equality symbol.” Scott never published his result, and a fully detailed proof first appeared in Karp [1964]. The approach to the theorem adopted here is based on the account given in Dickmann [1975].