We consider extensions of the language of Peano arithmetic by transfinitely iterated truth
definitions satisfying uniform Tarskian biconditionals. Without further axioms, such theories …

We deal with the fragment of modal logic consisting of implications of formulas built up from
the variables and the constant 'true'by conjunction and diamonds only. The weaker …

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We study the transfinite sequence of topologies on the ordinal numbers that is obtained
through successive closure under Cantor's derivative operator on sets of ordinals, starting …

We determine the strictly positive fragment QPL+(HA) of the quantified provability logic QPL
(HA) of Heyting Arithmetic. We show that QPL+(HA) is decidable and that it coincides with …

For any ordinal Λ, we can define a polymodal logic GLPΛ, with a modality [ξ] for each ξ< Λ.
These represent provability predicates of increasing strength. Although GLPΛ has no Kripke …

Provability logics are modal or polymodal systems designed for modeling the behavior of
Gödel's provability predicate and its natural extensions. If Λ is any ordinal, the Gödel-Löb …

We consider the well-known provability logic GLP. We prove that the GLP-provability
problem for polymodal formulas without variables is PSPACE-complete. For a number n, let …

Turing progressions have been often used to measure the proof-theoretic strength of
mathematical theories: iterate adding consistency of some weak base theory until you “hit” …

Given a computable ordinal Λ, the transfinite provability logic GLP Λ has for each ξ< Λ a
modality [ξ] intended to represent a provability predicate within a chain of increasing …