Countable homogeneous and partially homogeneous ordered structures
نویسنده
چکیده
I survey classification results for countable homogeneous or ‘partially homogeneous’ ordered structures. This includes some account of Schmerl’s classification of the countable homogeneous partial orders, outlining an extension of this to the coloured case, and also treating results on linear orders, and their generalizations, trees and cycle-free partial orders. 2000 Mathematics Subject Classification 06F99 keywords: partial ordering, tree, homogeneous
منابع مشابه
5 Universal homogeneous causal sets
Causal sets are particular partially ordered sets which have been proposed as a basic model for discrete space-time in quantum gravity. We show that the class C of all countable past-finite causal sets contains a unique causal set (U,≤) which is universal (i.e., any member of C can be embedded into (U,≤)) and homogeneous (i.e., (U,≤) has maximal degree of symmetry). Moreover, (U,≤) can be const...
متن کاملAge and weak indivisibility
Let H be a countable infinite homogeneous relational structure. If H is indivisible then it is weakly indivisible and if it is weakly indivisible then it is age indivisible. There are examples of countable infinite homogeneous structures which are weakly indivisible but not indivisible. It is a natural question to ask for examples of countable age indivisible homogenous structures which are not...
متن کاملA Universal Structure for Jv-free Graphs
Countable homogeneous graphs have been classified by Alistair Lachlan and Robert Woodrow [5,11]. There is a countable bipartite graph called the universal 'homogeneous' bipartite graph. However, this graph does not occur in Lachlan and Woodrow's list, because it is not homogeneous as a graph but only as a graph with a fixed bipartition (Cameron [1]). In this paper, I describe a graph which is a...
متن کاملHomogeneous Structures
A relational first order structure is homogeneous if every isomorphism between finite substructures extends to an automorphism. Familiar examples of such structures include the rational numbers with the usual order relation, the countable random and so called Rado graph, and many others. Countable homogeneous structures arise as Fraı̈ssé limits of amalgamation classes of finite structures, and h...
متن کاملCountable Homogeneous Lattices
We show that there are uncountably many countable homogeneous lattices. We give a discussion of which such lattices can be modular or distributive. The method applies to show that certain other classes of structures also have uncountably many homogeneous members.
متن کامل