Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simultaneously vanishing higher derived limits   In 1988, Sibe Marde\v{s}i\'{c} and Andrei Prasolov isolated an inverse system
$\mathbf{A}$ with the property that the additivity of strong homology on any
class of spaces which includes the closed subsets of Euclidean space would
entail that $\lim^n\mathbf{A}$ (the $n^{\text{th}}$ derived limit of
$\mathbf{A}$) vanishes for every $n >0$. Since that time, the question of
whether it is consistent with the $\mathsf{ZFC}$ axioms that $\lim^n
\mathbf{A}=0$ for every $n >0$ has remained open. It remains possible as well
that this condition in fact implies that strong homology is additive on the
category of metric spaces.
  We show that, assuming the existence of a weakly compact cardinal, it is
indeed consistent with the $\mathsf{ZFC}$ axioms that $\lim^n \mathbf{A}=0$ for
all $n >0$. We show this via a finite support iteration of Hechler forcings
which is of weakly compact length. More precisely, we show that in any forcing
extension by this iteration a condition equivalent to $\lim^n\mathbf{A}=0$ will
hold for each $n>0$. This condition is of interest in its own right; namely, it
is the triviality of every coherent $n$-dimensional family of certain specified
sorts of partial functions $\mathbb{N}^2\to\mathbb{Z}$ which are indexed in
turn by $n$-tuples of functions $f:\mathbb{N}\to\mathbb{N}$. The triviality and
coherence in question here generalize the well-studied case of $n=1$.

15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph