2 citations · 3 across the 3 of their papers we have counts for
3 papers
Predicativity through transfinite reflection
Andrés Cordon Franco, David Fernández Duque, Joost J. Joosten +1
Peano Arithmetic is known to be provably equivalent to reflection over Elementary Arithmetic. We prove a characterization of Predicative Analysis in the guise of ATR0 in terms of s…
Hyperations, Veblen progressions and transfinite iterations of ordinal functions
David Fernández-Duque, Joost J. Joosten
In this paper we introduce hyperations and cohyperations, which are forms of transfinite iteration of ordinal functions. Hyperations are iterations of normal functions. Unlike iter…
Models of transfinite provability logic
David Fernández-Duque, Joost J. Joosten
For any ordinal Λ, we can define a polymodal logic GLP(Λ), with a modality [ξ] for each ξ<Λ. These represent provability predicates of increasing strength. Although GLP(Λ) has no K…