Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decomposition of sets in real algebraic geometry   We present a new notion of decomposition of semialgebraic sets by introducing
a mode of irreducibility based on arc-analytic functions. The result is a
refinement of the decomposition of such sets with respect to the Zariski
topology as well as a refinement of the decomposition in each of the recent
approaches based on Nash and continuous rational functions. In addition, by
pairing the ring of arc-analytic functions with semialgebraic sets, we obtain a
theory of algebraic geometry equipped with strong tools such as the Identity
Principle and the Nullstellensatz.

34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc