Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial and model-theoretical principles related to regularity of
  ultrafilters and compactness of topological spaces. IV   We extend to singular cardinals the model-theoretical relation $\lambda
\stackrel{\kappa}{\Rightarrow} \mu$ introduced in P. Lipparini, The compactness
spectrum of abstract logics, large cardinals and combinatorial principles,
Boll. Unione Matematica Italiana ser. VII, {\bf 4-B} 875--903 (1990). We extend
some results obtained in Part II, finding equivalent conditions involving
uniformity of ultrafilters and the existence of certain infinite matrices. Our
present definition suggests a new compactness property for abstract logics.

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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
3
The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol