Notes on monadic logic. A: Monadic theory of the real line
In an earlier paper with \textit{Yu. Gurevich} [ibid. 49, 55-68 (1984; Zbl 0575.03028)] the author showed that (assuming CH) the second-order theory of the continuum in the Cohen extension of the universe has an interpretation in the monadic theory of the real line as well as in the monadic theory of any non-modest short chain. In this paper the author shows how this result can be obtained without CH.
monadic theory of non-modest short chain
scientific article; zbMATH DE number 4085636
scientific article