13 citations · 72 across the 24 of their papers we have counts for
6 papers · 2 filters
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…
Non-finite axiomatizability of Dynamic Topological Logic
David Fernández-Duque
Dynamic topological logic (DTL) is a polymodal logic designed for reasoning about {\em dynamic topological systems. These are pairs (X,f), where X is a topological space and f:X->X…
The polytopologies of transfinite provability logic
David Fernández-Duque
Provability logics are modal or polymodal systems designed for modeling the behavior of Gödel's provability predicate in arithmetical theories and its natural extensions. If Λis an…
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…