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 …

We introduce the logics GLP Λ, a generalization of Japaridze's polymodal provability logic
GLP ω where Λ is any linearly ordered set representing a hierarchy of provability operators …

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 …

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” …

This article studies the transfinite propositional provability logics GLP Λ and their
corresponding algebras. These logics have for each ordinal ξ< Λ a modality˂ ξ˃. We will …

Let T be a second-order arithmetical theory, Λ a well-order, λ< Λ and X⊆ ℕ. We use by the
weaker ECA0, the second-order analogue of Elementary Arithmetic. Thus we characterize …

arXiv:1605.08867v3 [math.LO] 3 Oct 2017 Page 1 arXiv:1605.08867v3 [math.LO] 3 Oct 2017
Worms and Spiders: Reflection Calculi and Ordinal Notation Systems David Fernández-Duque …

Fixing some computably enumerable theory TT, the Friedman-Goldfarb-Harrington (FGH)
theorem says that over elementary arithmetic, each\varSigma _1 Σ 1 formula is equivalent to …

This paper studies the transfinite propositional provability logics $\glp_\Lambda $ and their
corresponding algebras. These logics have for each ordinal $\xi<\Lambda $ a modality …

Given a set X of natural numbers, we may formalize “The formula φ is provable in ω-logic
over the theory T using an oracle for X” by a formula [∞| X] T φ in the language of second …