ON THE MONADIC SECOND-ORDER TRANSDUCTION HIERARCHY
We compare classes of finite relational structures via monadic second-order transductions. More precisely, we study the preorder where we set C subset of K if, and only if, there exists a transduction tau such that C subset of tau(K). If we only consider classes of incidence structures we can completely describe the resulting hierarchy. It is linear of order type omega+3. Each level can be characterised in terms of a suitable variant of tree-width. Canonical representatives of the various levels are: the class of all trees of height n, for each n is an element of N, of all paths, of all trees, and of all grids.
transductions monadic second-order logic guarded second-order logic hypergraphs