Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Open induction in a bounded arithmetic for TC^0   The elementary arithmetic operations $+,\cdot,\le$ on integers are well-known
to be computable in the weak complexity class $\mathrm{TC}^0$, and it is a
basic question what properties of these operations can be proved using only
$\mathrm{TC}^0$-computable objects, i.e., in a theory of bounded arithmetic
corresponding to $\mathrm{TC}^0$. We will show that the theory $\mathit{VTC}^0$
extended with an axiom postulating the totality of iterated multiplication
(which is computable in $\mathrm{TC}^0$) proves induction for quantifier-free
formulas in the language $\langle +,\cdot,\le \rangle$ (IOpen), and more
generally, minimization for $\Sigma^b_0$ formulas in the language of Buss's
$S_2$.

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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga