6 citations · 8 across the 5 of their papers we have counts for
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A Walk with Goodstein and Ackermann
David Fernández-Duque, Andreas Weiermann
Goodstein's theorem states that a certain sequences based on exponential notation for the natural numbers are always finite. The result is independent of Peano arithmetic and is a…
Untangled: A Complete Dynamic Topological Logic
David Fernández-Duque, Yoàv Montacute
Dynamic topological logic () is a trimodal logic designed for reasoning about dynamic topological systems. It was shown by Fernández-Duque that the natural set of axi…
Fundamental sequences and fast-growing hierarchies for the Bachmann-Howard ordinal
David Fernández-Duque, Andreas Weiermann
We prove that Buchholz's system of fundamental sequences for the function enjoys various regularity conditions, including the Bachmann property. We partially extend the…
Intermediate Goodstein principles
David Fernández-Duque, Oriola Gjetaj, Andreas Weiermann
The original Goodstein process proceeds by writing natural numbers in nested exponential -normal form, then successively raising the base to and subtracting one from the e…
The many faces of omega-logic
David Fernández-Duque
We consider several formalizations in the language of second-order arithmetic of "The formula is a theorem of -logic", including some which have been studied in the literatu…