Abstract
Let D = be a relational system whereby D is a nonempty set and P i is an m i-ary relation on D. With D we associate the (weak) monadic second-order theory (W)MT[D] consisting of the first-order predicate calculus with individual variables ranging over D; monadic predicate variables ranging over (finite) subsets of D; monadic predicate quantifiers; and constants corresponding to P 1, P 2, ⋯ We will often use (W)MT[D] ambiguously to mean also the set of true sentences of (W)MT[D].
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