2 citations · 4 across the 9 of their papers we have counts for
7 papers · 1 filter
A tree rewriting system for the Reflection Calculus
Sofía Santiago-Fernández, Joost J. Joosten, David Fernández-Duque
The () is the fragment of the polymodal logic in the language whose formulas are built up from …
Metric fixed point theory and partial impredicativity
David Fernández-Duque, Paul Shafer, Henry Towsner +1
We show that the Priess-Crampe & Ribenboim fixed point theorem is provable in . Furthermore, we show that Caristi's fixed point theorem for both Baire and Borel fun…
Dynamic Tangled Derivative Logic of Metric Spaces
David Fernández-Duque, Yoàv Montacute
Dynamical systems are abstract models of interaction between space and time. They are often used in fields such as physics and engineering to understand complex processes, but due…
Non-deterministic Semantics for Dynamic Topological Logic
David Fernández-Duque
Dynamic Topological Logic () is a combination of {\em 4}, under its topological interpretation, and the temporal logic interpreted over…
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…