TITLE: Proof of Decidability of Monadic First Order Logic
QUESTION [5 upvotes]: I'm looking for the proof of decidability of Monadic FOL (i.e. FOL limited to predicate symbols of arity at most one and no function symbols).
In the Wikipedia page there are two references (dated 1915, 1922, both in German) but I couldn't find the English version of them. Besides, since decidability and "effective computation" was made precise in 30's (Church, Turing), I'm not sure these sources are the right ones.
Do you know any book/paper that have the proof (sketch)?
Edit: As pointed out by Achilles, it follows from the following proposition (proven in the book "The Classical Decision Problem"):
Proposition 6.2.1. Let $\psi$ be a relational monadic formula, possibly with equality, of quantifier-rank $q$ with $m$ predicates. If $\psi$ is satisfiable, then it has a model of cardinality at most $q2^m$.

REPLY [2 votes]: I am reading a paper that cites the following work for the exact complexity of satisfiability:
[1] H. Lewis, "Complexity results for classes of quantification formulas", Journal of Computer and System Sciences, vol. 21, pp. 317--353, 1980.
[2] S. Homer, "Structural properties of complete problems for exponential time", in Complexity Theory Retrospective II, L. Hemaspaandra and A. Selman, Eds. Springer-Verlag, 1997, ch. 6, pp. 135-154.
remarking that "strictly speaking, [1] shows that the satisfiability problem is $\mathbf{NE}$-complete, where $\mathbf{NE} = \bigcup_c\mathbf{NTIME}(2^{cn})$". From results of [2] it also follows that satisfiability is $\mathbf{NEXPTIME}$-complete.