In [17,19] Peter Hancock and Anton Setzer introduced rules to extend Martin-LÃ¶fâ€™s type theory in order to represent interactive programming. The rules essentially reflect the existence of weaklyâ€¦ (More)

We introduce the notion of state dependent interactive programs for Martin-LÃ¶f Type Theory. These programs are elements of coalgebras of an endofunctor on the presheaf category S â†’ Set. We prove theâ€¦ (More)

We argue classicaly. We identify a natural number with the set of its predecessors. Definition 0.1. Let n âˆˆ N, ~x, ~y âˆˆ N and M, N âŠ† N. ~x â‰¤ ~y :â‡” âˆ€i < n.xi â‰¤ yi ~x < ~y :â‡” ~x â‰¤ ~y âˆ§ ~x 6= ~y M :=â€¦ (More)

In this paper we introduce a notation system for the infinitary derivations occurring in the ordinal analysis of KP + Î 3-Reflection due to Michael Rathjen. This allows a finitary ordinal analysis ofâ€¦ (More)