Book ChapterDOI
Turing progressions and their well-orders
David Fernández Duque,Joost J. Joosten +1 more
- pp 212-221
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TLDR
It is seen how Turing progressions are closely related to the closed fragment of GLP, polymodal provability logic, and natural well-orders in GLP that characterize certain aspects of these Turing progressIONS are studied.Abstract:
We see how Turing progressions are closely related to the closed fragment of GLP, polymodal provability logic. Next we study natural well-orders in GLP that characterize certain aspects of these Turing progressions.read more
Citations
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Journal ArticleDOI
On Provability Logics with Linearly Ordered Modalities
TL;DR: A reduction of Japaridze’s polymodal provability logic GLPω is provided, yielding among other things a finitary proof of the normal form theorem for the variable-free fragment of GLPΛ and the decidability of GLpΛ for recursive orderings Λ.
Journal ArticleDOI
Topological completeness of the provability logic GLP
TL;DR: Some constructions to build nontrivial GLP-spaces are developed and it is shown that GLP is complete w.r.t. the class of all GLPs, whenever they satisfy all the axioms of GLP.
A Bibliography of Publications of Alan Mathison Turing
TL;DR: This bibliography records publications of Alan Mathison Turing (1912{ 1954).
Journal ArticleDOI
Models of transfinite provability logic
TL;DR: This paper shows how to extend constructions for arbitrary Λ to build a Kripke model and a topological model, and shows that is sound for both of these structures, as well as complete, provided Θ is large enough.
Book ChapterDOI
Topological interpretations of provability logic
TL;DR: A survey of the results on topological semantics of polymodal provability logic can be found in this paper, with a special emphasis on the recent work on topology models of poly-modal Provability Logic.
References
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Book
Systems of Logic Based on Ordinals
TL;DR: These documents can only be used for educational and research purposes (“Fair use”) as per U.S. Copyright law (text below).
Journal ArticleDOI
Provability interpretations of modal logic
TL;DR: In this article, the authors consider interpretations of modal logic in Peano arithmetic determined by an assignment of a sentencev * ofP to each propositional variablev. They show that a modal formula, χ, is valid if ψ* is a theorem ofP in each interpretation.
Journal ArticleDOI
Reflection principles and provability algebras in formal arithmetic
TL;DR: In this article, a study of reflection principles in fragments of formal Peano arithmetic and their applications to the comparison and classification of arithmetical theories is presented, where the reflection principle is applied to the classification of Peano arithmologies.
Journal ArticleDOI
Provability algebras and proof-theoretic ordinals, I
TL;DR: In this article, an algebraic approach to proof-theoretic analysis based on the notion of graded provability algebra is proposed, that is, Lindenbaum boolean algebra of a theory enriched by additional operators which allow for the structure to capture syntactic sensitive information.
Journal Article
Veblen hierarchy in the context of provability algebras
TL;DR: In this paper, an extension of Japaridze's polymodal logic GLP with transfinitely many modalities is studied and a provability-algebraic ordinal notation system up to the ordinal 0 is developed.