GÖDEL’S SECOND INCOMPLETENESS THEOREM: HOW IT IS DERIVED AND WHAT IT DELIVERS

DOI10.1017/bsl.2020.22zbMath1462.03026OpenAlexW3034490412MaRDI QIDQ4984860

Saeed Salehi

Publication date: 21 April 2021

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

Full work available at URL: https://doi.org/10.1017/bsl.2020.22

zbMATH Keywords

second incompleteness theoremBoolos' proofChaitin's proofKleene's prooffirst incompleteness theoremRosser's proofGödel's proof

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Gödel numberings and issues of incompleteness (03F40) Algorithmic randomness and dimension (03D32)

Cites Work

• Nonstandard models and Kripke's proof of the Gödel theorem
• Self-reference and modal logic
• A note of provability, truth and existence
• On constructivity and the Rosser property: a closer look at some Gödelean proofs
• A remark on equivalent Rosser sentences
• General recursive functions of natural numbers
• Undecidable theories
• Necessary and Sufficient Conditions for Undecidability of the Gödel Sentence and its Truth
• On proofs of the incompleteness theorems based on Berry's paradox by Vopěnka, Chaitin, and Boolos
• Gödel–Rosser's Incompleteness Theorem, generalized and optimized for definable theories
• Reflection principles and provability algebras in formal arithmetic
• Rosser sentences
• Gödel's diagonalization technique and related properties of theories
• Σ_{𝑛}-bounding and Δ_{𝑛}-induction
• ANOTHER LOOK AT THE SECOND INCOMPLETENESS THEOREM
• Gödel’s Incompleteness Phenomenon—Computationally
• On weak completeness of intuitionistic predicate logic
• On axiomatizability within a system
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item