Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The first omega alephs: from simplices to trees of trees to higher walks   The point of departure for the present work is Barry Mitchell's 1972 theorem
that the cohomological dimension of $\aleph_n$ is $n+1$. We record a new proof
and mild strengthening of this theorem; our more fundamental aim, though, is
some clarification of the higher-dimensional infinitary combinatorics lying at
its core. In the course of this work, we describe simplicial characterizations
of the ordinals $\omega_n$, higher-dimensional generalizations of coherent
Aronszajn trees, bases for critical inverse systems over large index sets,
nontrivial $n$-coherent families of functions, and higher-dimensional
generalizations of portions of Todorcevic's walks technique. These
constructions and arguments are undertaken entirely within a $\mathsf{ZFC}$
framework; at their heart is a simple, finitely iterable technique of
compounding $C$-sequences.

7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat