Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cascades, Order and Ultrafilters   We investigate mutual behavior of cascades, contours of which are contained
in a fixed ultrafilter. Using that relation we prove (ZFC) that the class of
strict $J_{\omega^\omega}$-ultrafilters, introduced by J. E. Baumgartner in
\textit{Ultrafilters on $\omega$}, is empty. We translate the result to the
language of $<_\infty$-sequences under an ultrafilter, investigated by C.
Laflamme in \textit{A few special ordinal ultrafilters}, to show that if there
is an arbitrary long finite $<_\infty$-sequence under $u$ than $u$ is at least
strict $J_{\omega^{\omega+1}}$- ultrafilter.

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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
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The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas