Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Geometric Zero-One Law   Each relational structure X has an associated Gaifman graph, which endows X
with the properties of a graph. Suppose that X is infinite, connected and of
bounded degree. A first-order sentence in the language of X is almost surely
true (resp. a.s. false) for finite substructures of X if for every element x in
X, the fraction of substructures of the ball of radius n around x which satisfy
the sentence approaches 1 (resp. 0) as n approaches infinity. Suppose further
that, for every finite substructure, X has a disjoint isomorphic substructure.
Then every sentence is a.s. true or a.s. false for finite substructures of X.
This is one form of the geometric zero-one law. We formulate it also in a form
that does not mention the ambient infinite structure. In addition, we
investigate various questions related to the geometric zero-one law.

32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat