Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear extenders and the Axiom of Choice   In set theory without the axiom of Choice ZF, we prove that for every
commutative field IK, the following statement D_{\IK}: "On every non null
IK-vector space, there exists a non null linear form" implies the existence of
a IK-linear extender on every vector subspace of a $\IK$-vector space. This
solves a question raised in \cite{Mo09}. In the second part of the paper, we
generalize our results in the case of spherically complete ultrametric valued
fields, and show that Ingleton's statement is equivalent to the existence of
"isometric linear extenders".

13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio