Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterising Complexity Classes by Inductive Definitions in Bounded
  Arithmetic   Famous descriptive characterisations of P and PSPACE are restated in terms of
the Cook-Nguyen style second order bounded arithmetic. We introduce an axiom of
inductive definitions over second order bounded arithmetic. We show that P can
be captured by the axiom of inflationary inductive definitions whereas PSPACE
can be captured by the axiom of non-inflationary inductive definitions.

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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg