Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the geometric and differential properties of closed sets definable in
  quasianalytic structures   In this paper we show that the equivalences between certain properties of
closed subanalytic sets proved by E. Bierstone and P. Milman in \cite{[BM-1]}
hold for closed sets definable in quasianalytic o-minimal structures. In
particular we prove that uniform Chevalley estimate implies a stratification by
the diagram of initial exponents and further, Zariski semicontinuity of the
diagram of initial exponents. We also show that the stratification by the
diagram implies Zariski semicontinuity of Hilbert-Samuel function.

25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn