Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isomorphism and classification for countable structures   We introduce a topology on the space of all isomorphism types represented in
a given class of countable models, and use this topology as an aid in
classifying the isomorphism types. This mixes ideas from effective descriptive
set theory and computable structure theory, extending concepts from the latter
beyond computable structures to examine the isomorphism problem on arbitrary
countable structures. We give examples using specific classes of fields and of
trees, illustrating how the new concepts can yield classifications that reveal
differences between seemingly similar classes. Finally, we use a computable
homeomorphism to define a measure on the space of isomorphism types of
algebraic fields, and examine the prevalence of relative computable
categoricity under this measure.

8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph