Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractals and the monadic second order theory of one successor   We show that if $X$ is virtually any classical fractal subset of
$\mathbb{R}^n$, then $(\mathbb{R},<,+,X)$ interprets the monadic second order
theory of $(\mathbb{N},+1)$. This result is sharp in the sense that the
standard model of the monadic second order theory of $(\mathbb{N},+1)$ is known
to interpret $(\mathbb{R},<,+,X)$ for various classical fractals $X$ including
the middle-thirds Cantor set and the Sierpinski carpet. Let $X \subseteq
\mathbb{R}^n$ be closed and nonempty. We show that if the $C^k$-smooth points
of $X$ are not dense in $X$ for some $k \geq 1$, then $(\mathbb{R},<,+,X)$
interprets the monadic second order theory of $(\mathbb{N},+1)$. The same
conclusion holds if the packing dimension of $X$ is strictly greater than the
topological dimension of $X$ and $X$ has no affine points.

10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys