A Ramsey space of infinite polyhedra and the random polyhedron

In this paper we introduce a new topological Ramsey space whose elements are infinite ordered polyhedra. Then, we show as an application that the set of finite polyhedra satisfies two types of Ramsey property: one, when viewed as a category over \(\mathbb N\); the other, when considered as a class o...

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Bibliographic Details
Published in:arXiv.org 2016-02
Main Authors: Mijares, Jose G, Padilla, Gabriel
Format: Article
Language:English
Subjects:
Automorphisms
Polyhedra
Subspaces
Topology
Online Access:Get full text
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Summary:In this paper we introduce a new topological Ramsey space whose elements are infinite ordered polyhedra. Then, we show as an application that the set of finite polyhedra satisfies two types of Ramsey property: one, when viewed as a category over \(\mathbb N\); the other, when considered as a class of finite structures. The (ordered) random polyhedron is the Fraisse limit of the class of finite ordered polyhedra; we prove that its group of automorphisms is extremely amenable. Finally, we present a countably infinite family of topological Ramsey subspaces; each one determines a class of finite ordered structures which turns out to be a Ramsey class. One of these subspaces is Ellentuck's space; another one is associated to the class of finite ordered graphs whose Fraisse limit is the random graph. The Fraisse limits of these classes are not pairwise isomorphic as countable structures and none of them is isomorphic to the random polyhedron.
ISSN:2331-8422