Existentially closed structures and Gödel's second incompleteness theorem

DOI10.2307/2694926zbMath0981.03043OpenAlexW2053241037MaRDI QIDQ2732285

Zofia Adamowicz, Teresa Bigorajska

Publication date: 11 March 2002

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

Full work available at URL: https://doi.org/10.2307/2694926

zbMATH Keywords

second incompleteness theoremexistentially closed models

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Models of arithmetic and set theory (03C62)

Related Items

Partial collapses of the \(\Sigma _1\) complexity hierarchy in models for fragments of bounded arithmetic, Restricted polynomial induction versus ordinary induction, The incompleteness theorems after 70 years, Preservation theorems and restricted consistency statements in bounded arithmetic, Passive induction and a solution to a Paris-Wilkie open question, Semi-honest subrecursive degrees and the collection rule in arithmetic, The Axiom System IΣ0 Manages to Simultaneously Obey and Evade the Herbrandized Version of the Second Incompleteness Theorem, The scope of Gödel's first incompleteness theorem, A note on Σ₁-maximal models, Some specially formulated axiomizations for \(\mathrm{I}\Sigma _0\) manage to evade the Herbrandized version of the second incompleteness theorem, CURRENT RESEARCH ON GÖDEL’S INCOMPLETENESS THEOREMS

Cites Work

• Overspill and fragments of arithmetic
• Kolmogorov complexity and the second incompleteness theorem
• Other Proofs of Old Results
• A Note on Boolos' Proof of the Incompleteness Theorem
• On the incompleteness theorems