Sub-arithmetical ultrapowers: A survey

DOI10.1016/0168-0072(90)90064-9zbMath0724.03024OpenAlexW2068573065MaRDI QIDQ2276952

Thomas G. McLaughlin

Publication date: 1990

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-0072(90)90064-9

zbMATH Keywords

surveyminimalityend extensionsisolsexistential completenessNerode semiringscofinal extensionsfragments of true arithmeticrigidnesssub-arithmetical ultrapower

Mathematics Subject Classification ID

Nonstandard models of arithmetic (03H15) Models of arithmetic and set theory (03C62) Recursive equivalence types of sets and structures, isols (03D50) Ultraproducts and related constructions (03C20)

Related Items

\(\Delta_{1}\) ultrapowers are totally rigid ⋮ A remark on pseudo proof systems and hard instances of the satisfiability problem ⋮ The Lattice of Computably Enumerable Vector Spaces ⋮ On the Minimality of Tame Models in the Isols ⋮ Eight problems about Nerode semirings (recursive ultrapowers) ⋮ Some observations on the substructure lattice of a Δ1 ultrapower ⋮ R.e. Prime powers and total rigidity ⋮ Recursive Fibers of RST Isols ⋮ Polynomial time ultrapowers and the consistency of circuit lower bounds ⋮ Existentially Incomplete Tame Models and a Conjecture of Ellentuck

Cites Work

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• Models of arithmetic and recursive functions
• Diophantine correct non-standard models in the isols
• On Unions of Chains of Models
• A Note on a Theorem of H. FRIEDMAN
• A note on the Mac Dowell-Specker theorem
• Some Properties of ∀∃ Models in the Isols
• Some Extension and Rearrangement Theorems For Nerode Semirings
• Models and types of Peano's arithmetic

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