On the Monadic Second-Order Transduction Hierarchy

We compare classes ofnite relational structures via monad ic second-order transductions. More precisely, we study the preorder where we set C v K if, and only if, there exists a transductionsuch that C � �(K). If we only consider classes of incidence structures we can completely describe the resulting hierarchy. It is linear of order type !+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 2 N, of all paths, of all trees, and of all grids.

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