Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal elementary end extensions   Suppose that ${\mathcal M}$ is a model of PA and ${\mathcal N}$ is a
countably generated elementary end extension of ${\mathcal M}$. Let ${\mathfrak
X}$ be the set of subsets of M that are coded by ${\mathcal N}$. Then
${\mathcal M}$ has a minimal elementary end extension that codes exactly the
same subsets of M that ${\mathcal N}$ does iff every set that is
$\Pi_1^0$-definable in $({\mathcal M},{\mathfrak X})$ is the union of countably
many sets that are $\Sigma_1^0$-definable.

29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat