Cut-elimination and interpolation for Ω-logic

Archive for Mathematical Logic 27 (2):161-175 (1988)
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Abstract

In 1978, Girard introducedβ-logic to generalizeω-logic. The basic category ofβ-logic is the categoryON of ordinals. For geometric structure reasons, Girard changed the basic categoryON into the more general categoryWF of well-founded orders (1983). The logic he obtained was calledΩ-logic. Here, we extend (unpublished) results ofβ-logic toΩ-logic.

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10.1007/bf01620764

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Proof Theory and Logical Complexity. [REVIEW]Helmut Pfeifer - 1991 - Annals of Pure and Applied Logic 53 (4):197.

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