On the logical complexity of cyclic arithmetic
We study the logical complexity of proofs in cyclic arithmetic ($\mathsf{CA}$), as introduced in Simpson '17, in terms of quantifier alternations of formulae occurring. Writing $C\Sigma_n$ for (the logical consequences of) cyclic proofs containing only $\Sigma_n$ formulae, our main result is th...
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| Format: | Article |
| Language: | English |
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Logical Methods in Computer Science e.V.
2020-01-01
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| Series: | Logical Methods in Computer Science |
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| Online Access: | https://lmcs.episciences.org/4818/pdf |