13 citations · 70 across the 51 of their papers we have counts for
6 papers · 2 filters
Pi^0_1 ordinal analysis beyond first order arithmetic
J. J. Joosten
In this paper we give an overview of an essential part of a Pi^0_1 ordinal analysis of Peano Arithmetic (PA) as presented by Beklemishev. This analysis is mainly performed within t…
Well-orders in the transfinite Japaridze algebra
David Fernández-Duque, Joost J. Joosten
This paper studies the transfinite propositional provability logics $\glp_Λ$ and their corresponding algebras. These logics have for each ordinal a modality $\la α\ra$. We w…
On provability logics with linearly ordered modalities
Lev D. Beklemishev, David Fernández-Duque, Joost J. Joosten
We introduce the logics GLP(Λ), a generalization of Japaridze's polymodal provability logic GLP(ω) where Λis any linearly ordered set representing a hierarchy of provability operat…
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…
Well-orders in the transfinite Japaridze algebra II: Turing progressions and their well-orders
David Fernández-Duque, Joost J. Joosten
We study transfinite extensions of Japaridze's provability logic GLP and the well-founded relations that naturally occur within them. Every ordinal induces a partial order over the…