On Extracting Variable Herbrand Disjunctions

Studia Logica 110 (4):1115-1134 (2022)
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Abstract

Some quantitative results obtained by proof mining take the form of Herbrand disjunctions that may depend on additional parameters. We attempt to elucidate this fact through an extension to first-order arithmetic of the proof of Herbrand’s theorem due to Gerhardy and Kohlenbach which uses the functional interpretation.

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10.1007/s11225-022-09990-5

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On the interpretation of non-finitist proofs–Part II.G. Kreisel - 1952 - Journal of Symbolic Logic 17 (1):43-58.
On the interpretation of non-finitist proofs—Part I.G. Kreisel - 1951 - Journal of Symbolic Logic 16 (4):241-267.
On n-quantifier induction.Charles Parsons - 1972 - Journal of Symbolic Logic 37 (3):466-482.

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