THE ∀∃ THEORY OF PEANO Σ1 SENTENCES

DOI10.1142/S0219061308000774zbMath1191.03005OpenAlexW2050976788MaRDI QIDQ5305060

V. Yu. Shavrukov

Publication date: 19 March 2010

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

Full work available at URL: https://doi.org/10.1142/s0219061308000774

zbMATH Keywords

arithmeticprovability logicSolovay functions\(\forall \exists \) theorylattice of \(\Sigma_1\) sentences

Mathematics Subject Classification ID

Logical aspects of lattices and related structures (03G10) Decidability of theories and sets of sentences (03B25) First-order arithmetic and fragments (03F30) Provability logics and related algebras (e.g., diagonalizable algebras) (03F45) Gödel numberings and issues of incompleteness (03F40)

Related Items (7)

Franco Montagna's work on provability logic and many-valued logic ⋮ Duality, non-standard elements, and dynamic properties of r.e. sets ⋮ Effectively inseparable Boolean algebras in lattices of sentences ⋮ ON SHAVRUKOV’S NON-ISOMORPHISM THEOREM FOR DIAGONALIZABLE ALGEBRAS ⋮ Interpretability degrees of finitely axiomatized sequential theories ⋮ Corrigendum: The ∀∃ theory of Peano Σ1 sentences ⋮ HIERARCHICAL INCOMPLETENESS RESULTS FOR ARITHMETICALLY DEFINABLE EXTENSIONS OF FRAGMENTS OF ARITHMETIC

Cites Work

• The intervals of the lattice of recursively enumerable sets determined by major subsets
• Provability interpretations of modal logic
• Classical recursion theory. Vol. II
• The elementary theory of recursively enumerable sets
• Mappings of closure relations
• Effectively inseparable Boolean algebras in lattices of sentences
• On elementary theories of some lattices or α-recursively enumerable sets
• Modal Logic, Transition Systems and Processes
• Decision problem for separated distributive lattices

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