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This article provides a language-theoretic rendering of Herbrand’s theorem. To each first-order proof is associated a higher-order recursion scheme that abstracts the computation of Herbrand sets obtained through Gentzen-style multicut elimination. The representation extends previous results in t...
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Recent work by Afshari et al. introduce a notion of Herbrand schemes for first-order logic by associating a higher-order recursion scheme to a sequent calculus proof. Calculating the language of associated Herbrand schemes directly yields Herbrand disjunctions. As such, these schemes can be seen ...
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Positionalism and antipositionalism, two apparently opposing views on relations, give different answers to the question how things can be arranged one way rather than another. In positionalism, relations come with positions to which objects may be assigned; in antipositionalism relations have no ...
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We prove that, for every antichain A in the poset of the finite subsets of omega, the set of maximal antichains which extend A has finite size or the size of the continuum. As a consequence we prove a conjecture of de Jongh and Vargas-Sandoval about nepfi families of finite languages.
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