Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Mitchell-like order for Ramsey and Ramsey-like cardinals   Smallish large cardinals $\kappa$ are often characterized by the existence of
a collection of filters on $\kappa$, each of which is an ultrafilter on the
subsets of $\kappa$ of some transitive $\mathrm{ZFC}^-$-model of size $
\kappa$. We introduce a Mitchell-like order for Ramsey and Ramsey-like
cardinals, ordering such collections of small filters. We show that the
Mitchell-like order and the resulting notion of rank have all the desirable
properties of the Mitchell order on normal measures on a measurable cardinal.
The Mitchell-like order behaves robustly with respect to forcing constructions.
We show that extensions with cover and approximation properties cannot increase
the rank of a Ramsey or Ramsey-like cardinal. We use the results about
extensions with cover and approximation properties together with recently
developed techniques about soft killing of large-cardinal degrees by forcing to
softly kill the ranks of Ramsey and Ramsey-like cardinals.

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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org