Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Star Height Hierarchy Vs. The Variable Hierarchy   The star height hierarchy (resp. the variable hierarchy) results in
classifying $\mu$-terms into classes according to the nested depth of fixed
point operators (resp. to the number of bound variables). We prove, under some
assumptions, that the variable hierarchy is a proper refinement of the star
height hierarchy. We mean that the non collapse of the variable hierarchy
implies the non collapse of the star height hierarchy. The proof relies on the
combinatorial characterization of the two hierarchies.

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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg