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- W2092553530 abstract "We propose two admissible closures $${mathbb{A}({sf PTCA})}$$ and $${mathbb{A}({sf PHCA})}$$ of Ferreira’s system PTCA of polynomial time computable arithmetic and of full bounded arithmetic (or polynomial hierarchy computable arithmetic) PHCA. The main results obtained are: (i) $${mathbb{A}({sf PTCA})}$$ is conservative over PTCA with respect to $${forallexistsSigma^b_1}$$ sentences, and (ii) $${mathbb{A}({sf PHCA})}$$ is conservative over full bounded arithmetic PHCA for $${forallexistsSigma^b_{infty}}$$ sentences. This yields that (i) the $${Sigma^b_1}$$ definable functions of $${mathbb{A}({sf PTCA})}$$ are the polytime functions, and (ii) the $${Sigma^b_{infty}}$$ definable functions of $${mathbb{A}({sf PHCA})}$$ are the functions in the polynomial time hierarchy." @default.
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- W2092553530 date "2011-05-04" @default.
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- W2092553530 title "Admissible closures of polynomial time computable arithmetic" @default.
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- W2092553530 doi "https://doi.org/10.1007/s00153-011-0238-7" @default.
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