Jordan groups and limits of betweenness relations

2006 ◽  
Vol 9 (1) ◽  
Author(s):  
Meenaxi Bhattacharjee ◽  
Dugald Macpherson
Keyword(s):  
Betweenness Relations

Transitive closure and betweenness relations

2001 ◽  
Vol 120 (3) ◽  
pp. 415-422 ◽  
Author(s):  
Dionis Boixader ◽  
Joan Jacas ◽  
Jordi Recasens
Keyword(s):  
Transitive Closure ◽  
Betweenness Relations

Betweenness relations and cycle-free partial orders

1996 ◽  
Vol 119 (4) ◽  
pp. 631-643 ◽  
Author(s):  
J. K. Truss
Keyword(s):  
Partial Order ◽  
Linear Order ◽  
Partial Orders ◽  
Partial Ordering ◽  
Macneille Completion ◽  
Alternative Definition ◽  
Betweenness Relations

The intuition behind the notion of a cycle-free partial order (CFPO) is that it should be a partial ordering (X, ≤ ) in which for any sequence of points (x0, x1;…, xn–1) with n ≤ 4 such that xi is comparable with xi+1 for each i (indices taken modulo n) there are i and j with j ╪ i, i + 1 such that xj lies between xi and xi+1. As its turn out however this fails to capture the intended class, and a more involved definition, in terms of the ‘Dedekind–MacNeille completion’ of X was given by Warren[5]. An alternative definition involving the idea of a betweenness relation was proposed by P. M. Neumann [1]. It is the purpose of this paper to clarify the connections between these definitions, and indeed between the ideas of semi-linear order (or ‘tree’), CFPO, and the betweenness relations described in [1]. In addition I shall tackle the issue of the axiomatizability of the class of CFPOs.

Archimedean actions on median pretrees

2001 ◽  
Vol 130 (3) ◽  
pp. 383-400 ◽  
Author(s):  
BRIAN H. BOWDITCH ◽  
JOHN CRISP
Keyword(s):  
Group Actions ◽  
General Setting ◽  
Countable Group ◽  
Convergence Group ◽  
Isometric Actions ◽  
Betweenness Relations

In this paper we consider group actions on generalized treelike structures (termed ‘pretrees’) defined simply in terms of betweenness relations. Using a result of Levitt, we show that if a countable group admits an archimedean action on a median pretree, then it admits an action by isometries on an ℝ-tree. Thus the theory of isometric actions on ℝ-trees may be extended to a more general setting where it merges naturally with the theory of right-orderable groups. This approach has application also to the study of convergence group actions on continua.

scholarly journals Betweenness of partial orders

2020 ◽  
Vol 54 ◽  
pp. 7
Author(s):  
Bruno Courcelle
Keyword(s):  
Partial Order ◽  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Second Order ◽  
Partial Orders ◽  
First Order ◽  
Betweenness Relations

We construct a monadic second-order sentence that characterizes the ternary relations that are the betweenness relations of finite or infinite partial orders. We prove that no first-order sentence can do that. We characterize the partial orders that can be reconstructed from their betweenness relations. We propose a polynomial time algorithm that tests if a finite relation is the betweenness of a partial order.

scholarly journals Betweenness Relations in a Categorical Setting

2017 ◽  
Vol 72 (1-2) ◽  
pp. 649-664 ◽  
Author(s):  
J. Bruno ◽  
A. McCluskey ◽  
P. Szeptycki
Keyword(s):  
Categorical Setting ◽  
Betweenness Relations
Sign in / Sign up

Export Citation Format

Share Document