Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Axiomatization of betweenness in order-theoretic trees   The ternary betweenness relation of a tree, B(x,y,z) expresses that y is on
the unique path between x and z. This notion can be extended to order-theoretic
trees defined as partial orders such that the set of nodes larger than any node
is linearly ordered. In such generalized trees, the unique "path" between two
nodes can have infinitely many nodes.
  We generalize some results obtained in a previous article for the betweenness
of join-trees. Join-trees are order-theoretic trees such that any two nodes
have a least upper-bound. The motivation was to define conveniently the
rank-width of a countable graph. We called quasi-tree the structure based on
the betweenness relation of a join-tree. We proved that quasi-trees are
axiomatized by a first-order sentence.
  Here, we obtain a monadic second-order axiomatization of betweenness in
order-theoretic trees. We also define and compare several induced betweenness
relations, i.e., restrictions to sets of nodes of the betweenness relations in
generalized trees of different kinds. We prove that induced betweenness in
quasi-trees is characterized by a first-order sentence. The proof uses
order-theoretic trees.

15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: eess
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
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The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: econ