The proofs presented in this paper afford further examples of what seems to be a quite general method for eliminating quantifiers in monadic second order theories. All known cases
of decidable MT-theories can be obtained by using this method. In Section 2 we outline the method, survey the results, and state outstanding problems, which seem accessible by our method. In Section 3 we show how the two versions of the method work in the classical case MT[W,<]. To implement the deterministic method, we present the important subset-construction of McNaughton [13], in a streamlined and more explicit version. In this form the construction will naturally extend to arbitrary ordinals aRead more at http://ebookee.org/Decidable-Theories-II_1085759.html#UmI5jpx6DyAsHaTf.99