Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Anomalous Semigroups and Real Numbers   Motivated by intuitive properties of physical quantities, the notion of a
non-anomalous semigroup is formulated. These are totally ordered semigroups
where there are no `infinitesimally close' elements. The real numbers are then
defined as the terminal object in a closely related category. From this
definition a field structure on $\mathbb R$ is derived, relating multiplication
to morphisms between non-anomalous semigroups.

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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int