On the Monadic Second-Order Transduction Hierarchy

Details On the Monadic Second-Order Transduction Hierarchy On the Monadic Second-Order Transduction Hierarchy

2010-04-27

arxiv.org/abs/1004.4777v4

LMCS 6 (2:2) 2010

Mathematics

Logic

Scientific paper

10.2168/LMCS-6(2:2)2010

We compare classes of finite relational structures via monadic second-order transductions. More precisely, we study the preorder where we set C \subseteq K if, and only if, there exists a transduction {\tau} such that C\subseteq{\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 \in N, of all paths, of all trees, and of all grids.

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