Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Examples in dependent theories   In the first part we show a counterexample to a conjecture by Shelah
regarding the existence of indiscernible sequences in dependent theories (up to
the first inaccessible cardinal). In the second part we discuss generic pairs,
and give an example where the pair is not dependent. Then we define the notion
of directionality which deals with counting the number of coheirs of a type and
we give examples of the different possibilities. Then we discuss
non-splintering, an interesting notion that appears in the work of Rami
Grossberg, Andr\'es Villaveces and Monica VanDieren, and we show that it is not
trivial (in the sense that it can be different than splitting) whenever the
directionality of the theory is not small. In the appendix we study dense types
in RCF.

12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph