21 citations · 43 across the 14 of their papers we have counts for
16 papers
Gödel-Dummett linear temporal logic
Juan Pablo Aguilera, Martín Diéguez, David Fernández-Duque +1
We investigate a version of linear temporal logic whose propositional fragment is Gödel-Dummett logic (which is well known both as a superintuitionistic logic and a t-norm fuzzy lo…
A Gödel Calculus for Linear Temporal Logic
Juan Pablo Aguilera, Martín Diéguez, David Fernández-Duque +1
We consider Gödel temporal logic (), a variant of linear temporal logic based on Gödel--Dummett propositional logic. In recent work, we have shown this logic to enjoy natu…
Time and Gödel: Fuzzy temporal reasoning in PSPACE
Juan Pablo Aguilera, Martín Diéguez, David Fernández-Duque +1
We investigate a non-classical version of linear temporal logic whose propositional fragment is Gödel--Dummett logic (which is well known both as a superintuitionistic logic and a…
Functorial Fast-Growing Hierarchies
J. P. Aguilera, F. Pakhomov, A. Weiermann
Fast-growing hierarchies are sequences of functions obtained through various processes similar to the ones that yield multiplication from addition, exponentiation from multiplicati…
The Consequences of a Theory
Juan P. Aguilera, Fedor Pakhomov
We develop the abstract framework for a proof-theoretic analysis of theories with scope beyond ordinal numbers, resulting in an analog of Ordinal Analysis aimed at the study of the…
Ackermann and Goodstein go functorial
Juan P. Aguilera, Anton Freund, Michael Rathjen +1
We present variants of Goodstein's theorem that are equivalent to arithmetical comprehension and to arithmetical transfinite recursion, respectively, over a weak base theory. These…
Long Games and -Projective Sets
Juan P. Aguilera, Sandra Müller, Philipp Schlicht
We prove a number of results on the determinacy of -projective sets of reals, i.e., those belonging to the smallest pointclass containing the open sets and closed under compleme…
Projective Games on the Reals
Juan P. Aguilera, Sandra Müller
Let denote the minimal active iterable extender model which has Woodin cardinals and contains all reals, if it exists, in which case we denote by $M_n(…
Determined Admissible Sets
Juan P. Aguilera
It is shown, from hypotheses in the region of Woodin cardinals, that there is a transitive model of KP + AD containing all reals.
The consistency strength of long projective determinacy
Juan P. Aguilera, Sandra Müller
We determine the consistency strength of determinacy for projective games of length . Our main theorem is that -determinacy for games of length imp…
The Order of Reflection
J. P. Aguilera
Extending Aanderaa's classical result that , we determine the order between any two patterns of iterated - and -reflection. We show that this \emph{linea…
Games and Reflection in
J. P. Aguilera
It is shown that determinacy of games of length is equivalent to the existence of a transitive model of KP + AD which contains the reals and reflects facts about…
Long Borel Games
J. P. Aguilera
It is shown that Borel games of length are determined if, and only if, for every countable ordinal , there is a fine-structural, countably iterable extender model of Zerme…
A Topological Completeness Theorem for Transfinite Provability Logic
Juan P. Aguilera
We prove a topological completeness theorem for the modal logic GLP containing operators for Ord intended to capture progressively stronger notions of cons…
Unsound Inferences Make Proofs Shorter
Juan P. Aguilera, Matthias Baaz
We give examples of calculi that extend Gentzen's sequent calculus LK by unsound quantifier inferences in such a way that (i) derivations lead only to true sequents, and (ii) proof…
Strong Completeness of Provability Logic for Ordinal Spaces
Juan P. Aguilera, David Fernández-Duque
Abashidze and Blass independently proved that the modal logic is complete for its topological interpretation over any ordinal greater than or equal to equipped with…