Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform Model Completeness for the Real Field with the Weierstrass $\wp$
  Function   In this work is we prove model completeness for the expansion of the real
field by the Weierstrass $\wp$ function as a function of the variable $z$ and
the parameter (or period) $\tau$. We need to existentially define the partial
derivatives of the $\wp$ function with respect to the variable $z$ and the
parameter $\tau$. In order to obtain this result we need to include in the
structure function symbols for the unrestricted exponential function and
restricted sine function, the Weierstrass $\zeta$ function and the quasimodular
form $E_2$. We prove some auxiliary model completeness results with the same
functions composed with appropriate change of variables. In the conclusion we
make some remarks about the noneffectiveness of our proof and the difficulties
to be overcome to obtain an effective model completeness result.

11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
16
The categories of this paper are: stat