On strong provability predicates and the associated modal logics

DOI10.2307/2275337zbMath0795.03082OpenAlexW2065285281MaRDI QIDQ5287692

Konstantin N. Ignatiev

Publication date: 17 August 1993

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2275337

zbMATH Keywords

fixed point propertyCraig interpolation lemmastrong provability predicatejoint provability logic for iterated \(\omega\)-provability

Mathematics Subject Classification ID

Modal logic (including the logic of norms) (03B45) First-order arithmetic and fragments (03F30) Gödel numberings and issues of incompleteness (03F40)

Related Items (24)

Provability algebras and proof-theoretic ordinals. I ⋮ On elementary theories of ordinal notation systems based on reflection principles ⋮ Positive provability logic for uniform reflection principles ⋮ Deducibility and independence in Beklemishev's autonomous provability calculus ⋮ The omega-rule interpretation of transfinite provability logic ⋮ PREDICATIVITY THROUGH TRANSFINITE REFLECTION ⋮ Linear $ \mathrm{GLP}$-algebras and their elementary theories ⋮ Kripke semantics for provability logic GLP ⋮ Provability and interpretability logics with restricted realizations ⋮ On the positive fragment of the polymodal provability logic GLP ⋮ Reflection calculus and conservativity spectra ⋮ On provability logics with linearly ordered modalities ⋮ The polytopologies of transfinite provability logic ⋮ Axiomatizing provable \(n\)-provability ⋮ On the complexity of the closed fragment of Japaridze's provability logic ⋮ Derived topologies on ordinals and stationary reflection ⋮ Turing-Taylor expansions for arithmetic theories ⋮ A simplified proof of arithmetical completeness theorem for provability logic GLP ⋮ Interpolation properties for provability logics GL and GLP ⋮ AXIOMATIZATION OF PROVABLE n-PROVABILITY ⋮ Conservativity spectra and Joosten-Fernández model ⋮ Topological Interpretations of Provability Logic ⋮ MÜNCHHAUSEN PROVABILITY ⋮ HIERARCHICAL INCOMPLETENESS RESULTS FOR ARITHMETICALLY DEFINABLE EXTENSIONS OF FRAGMENTS OF ARITHMETIC

Cites Work

• Unnamed Item
• Omega-consistency and the diamond
• Provability interpretations of modal logic
• The interpretability logic of Peano arithmetic

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