Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Between Whitehead groups and uniformization   For a given stationary set $S$ of countable ordinals we prove (in
$\mathbf{ZFC}$) that the assertion "every $S$-ladder system has
$\aleph_0$-uniformization" is equivalent to "every strongly $\aleph_1$-free
abelian group of cardinality $\aleph_1$ with non-freeness invariant $\subseteq
S$ is $\aleph_1$-coseparable, i.e. Ext$(G, \oplus_{i=0}^{\infty} \mathbb Z)=0$
(in particular Whitehead, i.e.\ Ext$(G, \mathbb Z)=0$)". This solves problems
B3 and B4 from Eklof and Mekler's book.

33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an