Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Definable V-topologies, Henselianity and NIP   We initiate the study of definable V-topolgies and show that there is at most
one such V-topology on a t-henselian NIP field. Equivalently, we show that if
$(K,v_1,v_2)$ is a bi-valued NIP field with $v_1$ henselian (resp. t-henselian)
then $v_1$ and $v_2$ are comparable (resp. dependent).
  As a consequence Shelah's conjecture for NIP fields implies the henselianity
conjecture for NIP fields. Furthermore, the latter conjecture is proved for any
field admitting a henselian valuation with a dp-minimal residue field.
  We conclude by showing that Shelah's conjecture is equivalent to the
statement that any NIP field not contained in the algebraic closure of a finite
field is t-henselian.

13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat