منابع مشابه
First order convergence of matroids
The model theory based notion of the first order convergence unifies the notions of the left-convergence for dense structures and the BenjaminiSchramm convergence for sparse structures. It is known that every first order convergent sequence of graphs with bounded tree-depth can be represented by an analytic limit object called a limit modeling. We establish the matroid counterpart of this resul...
متن کاملDeciding first order logic properties of matroids
Frick and Grohe [J. ACM 48 (2006), 1184–1206] introduced a notion of graph classes with locally bounded tree-width and established that every first order logic property can be decided in almost linear time in such a graph class. Here, we introduce an analogous notion for matroids (locally bounded branch-width) and show the existence of a fixed parameter algorithm for first order logic propertie...
متن کاملFirst-Order Convergence and Roots
Nešetřil and Ossona de Mendez introduced the notion of first order convergence, which unifies the notions of convergence for sparse and dense graphs. They asked whether if (Gi)i∈N is a sequence of graphs with M being their first order limit and v is a vertex of M , then there exists a sequence (vi)i∈N of vertices such that the graphs Gi rooted at vi converge to M rooted at v. We show that this ...
متن کاملDimensions, matroids, and dense pairs of first-order structures
A structure M is pregeometric if the algebraic closure is a pregeometry in all M ′ elementarily equivalent to M . We define a generalisation: structures with an existential matroid. The main examples are superstable groups of U-rank a power of ω and d-minimal expansion of fields. Ultraproducts of pregeometric structures expanding a field, while not pregeometric in general, do have an unique exi...
متن کاملDimension , matroids , and dense pairs of first - order structures
A structure M is pregeometric if the algebraic closure is a pregeometry in all M ′ elementarily equivalent to M . We define a generalisation: structures with an existential matroid. The main examples are superstable groups of U-rank a power of ω and d-minimal expansion of fields. Ultraproducts of pregeometric structures expanding a field, while not pregeometric in general, do have an unique exi...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2017
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2016.08.005