Cut-elimination and Interpolation for the Omega-Logic

Jacqueline Vauzeilles (1)

1 ELM - Équipe de Logique Mathématique

In 1978, Girard introduced the beta-logic to generalize the omega-logic. The basic category of beta-logic is the category ON of ordinals. For geometric structure reasons, Girard changed the basic theory ON into the more general category WF of well-founded orders (1983). The logic he obtained was called Omega-logic. Here, we extend (unpublished) results of beta-logic to Omega-logic.

Domaines: Logique [math.LO]; Logique en informatique [cs.LO]

Jacqueline Vauzeilles. Cut-elimination and Interpolation for the Omega-Logic. Archive for Mathematical Logic, 1988, 27, pp.161-175. ⟨hal-00003514⟩