Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On perturbations of Hilbert spaces and probability algebras with a
  generic automorphism   We prove that $IHS_A$, the theory of infinite dimensional Hilbert spaces
equipped with a generic automorphism, is $\aleph_0$-stable up to perturbation
of the automorphism, and admits prime models up to perturbation over any set.
Similarly, $APr_A$, the theory of atomless probability algebras equipped with a
generic automorphism is $\aleph_0$-stable up to perturbation. However, not
allowing perturbation it is not even superstable.

3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol