Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High dimensional Ellentuck spaces and initial chains in the Tukey
  structure of non-p-points   The generic ultrafilter $\mathcal{G}_2$ forced by
$\mathcal{P}(\omega\times\omega)/($Fin$\otimes$Fin) was recently proved to be
neither maximum nor minimum in the Tukey order of ultrafilters (in a recent
paper of Blass, Dobrinen, and Raghavan), but it was left open where exactly in
the Tukey order it lies. We prove that $\mathcal{G}_2$ is in fact Tukey minimal
over its projected Ramsey ultrafilter. Furthermore, we prove that for each
$k\ge 2$, the collection of all nonprincipal ultrafilters Tukey reducible to
the generic ultrafilter $\mathcal{G}_k$ forced by
$\mathcal{P}(\omega^k)/$Fin$^{\otimes k}$ forms a chain of length $k$.
Essential to the proof is the extraction of a dense subset $\mathcal{E}_k$ from
(Fin$^{\otimes k})^+$ which we prove to be a topological Ramsey space. The
spaces $\mathcal{E}_k$, $k\ge 2$, form a hiearchy of high dimensional Ellentuck
spaces. New Ramsey-classification theorems for equivalence relations on fronts
on $\mathcal{E}_k$ are proved, extending the Pudlak-Rodl Theorem for fronts on
the Ellentuck space, which are applied to find the Tukey structure below
$\mathcal{G}_k$.

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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th