First order convergence of matroids

نویسندگان

  • Frantisek Kardos
  • Daniel Král
  • Anita Liebenau
  • Lukás Mach
چکیده

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 result: every first order convergent sequence of matroids with bounded branch-depth representable over a fixed finite field has a limit modeling, i.e., there exists an infinite matroid with the elements forming a probability space that has asymptotically the same first order properties. We show that neither of the bounded branch-depth assumption nor the representability assumption can be removed.

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عنوان ژورنال:
  • Eur. J. Comb.

دوره 59  شماره 

صفحات  -

تاریخ انتشار 2017