منابع مشابه
Infinite Gammoids
Finite strict gammoids, introduced in the early 1970’s, are matroids defined via finite digraphs equipped with some set of sinks: a set of vertices is independent if it admits a linkage to these sinks. In particular, an independent set is maximal (i.e. a base) precisely if it is linkable onto the sinks. In the infinite setting, this characterization of the maximal independent sets need not hold...
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We introduce the concept of flatness degree for matroids, as a generalization of submodularity. This represents weaker variations of the concept of flatness which characterize strict gammoids for finite matroids. We prove that having flatness degree 3, which is the smallest non-trivial flatness degree, implies pseudomodularity on the lattice of flats of the matroid. We show however an example o...
متن کاملInfinite Gammoids: Minors and Duality
This sequel to Afzali Borujeni et. al. (2015) considers minors and duals of infinite gammoids. We prove that the class of gammoids defined by digraphs not containing a certain type of substructure, called an outgoing comb, is minor-closed. Also, we prove that finite-rank minors of gammoids are gammoids. Furthermore, the topological gammoids of Carmesin (2014) are proved to coincide, as matroids...
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Using countable support iteration of S-proper posets, for some appropriate stationary set S, we obtain a generic extension of the constructible universe, in which b = c = א2 and there is a maximal cofinitary group with a Π2-definable set of generators.
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Let κ be an arbitrary regular infinite cardinal and let C denote the set of κ-maximal cofinitary groups. We show that if GCH holds and C is a closed set of cardinals such that 1. κ ∈ C, ∀ν ∈ C(ν ≥ κ), 2. if |C| ≥ κ then [κ, |C|] ⊆ C, 3. ∀ν ∈ C(cof(ν) ≤ κ→ ν ∈ C), then there is a generic extension in which cofinalities have not been changed and such that C = {|G| : G ∈ C}. The theorem generalize...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2016
ISSN: 0166-218X
DOI: 10.1016/j.dam.2015.07.030