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 Here, we extend (unpublished) results ofβ-logic toΩ-logic.
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Vauzeilles, J. Cut-elimination and interpolation for Ω-logic. Arch Math Logic 27, 161–175 (1988). https://doi.org/10.1007/BF01620764
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DOI: https://doi.org/10.1007/BF01620764