No abstract

No abstract

Abstract. We compare classes of finite relational structures via monadic second-order transductions. More precisely, we study the preorder where we set C ⊑ K if, and only if, there exists a transduction τ such that C ⊆ τ (K). If we only consider classes of incidence structures we can completely describe the resulting hierarchy. It is linear of order type ω+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 ∈ N, of all paths, of all trees, and of all grids.

International audienc

Aiming for applications in monadic second-order model theory, we study first-order theories without definable pairing functions. Our main results concern forking-properties of sequences of indiscernibles. These turn out to be very well-behaved for the theories under consideration.