Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal sequences for the order-automorphisms of the rationals   In this paper, we consider the group Aut$(\mathbb{Q}, \leq)$ of
order-automorphisms of the rational numbers, proving a result analogous to a
theorem of Galvin's for the symmetric group. In an announcement, Kh\'elif
states that every countable subset of Aut$(\mathbb{Q}, \leq)$ is contained in
an $N$-generated subgroup of Aut$(\mathbb{Q}, \leq)$ for some fixed
$N\in\mathbb{N}$. We show that the least such $N$ is $2$. Moreover, for every
countable subset of Aut$(\mathbb{Q}, \leq)$, we show that every element can be
given as a prescribed product of two generators without using their inverses.
More precisely, suppose that $a$ and $b$ freely generate the free semigroup
$\{a,b\}^+$ consisting of the non-empty words over $a$ and $b$. Then we show
that there exists a sequence of words $w_1, w_2,\ldots$ over $\{a,b\}$ such
that for every sequence $f_1, f_2, \ldots\in\,$Aut$(\mathbb{Q}, \leq)$ there is
a homomorphism $\phi:\{a,b\}^{+}\to$ Aut$(\mathbb{Q},\leq)$ where
$(w_i)\phi=f_i$ for every $i$.
  As a corollary to the main theorem in this paper, we obtain a result of
Droste and Holland showing that the strong cofinality of Aut$(\mathbb{Q},
\leq)$ is uncountable, or equivalently that Aut$(\mathbb{Q}, \leq)$ has
uncountable cofinality and Bergman's property.

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The categories of this paper are: hep-ph
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th