Primes and their residue rings in models of open induction

DOI10.1016/0168-0072(89)90025-0zbMath0675.03040OpenAlexW1965416269MaRDI QIDQ1121883

David Marker, Angus J. Macintyre

Publication date: 1989

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(89)90025-0

zbMATH Keywords

independence resultsprime numbersordered fieldordered ringsresidue fieldinfinite primesmodels for open induction

Mathematics Subject Classification ID

Nonstandard models of arithmetic (03H15) Models of arithmetic and set theory (03C62) Nonstandard arithmetic (number-theoretic aspects) (11U10) Nonstandard arithmetic and field theory (12L15)

Related Items (14)

Some weak fragments of HA and certain closure properties ⋮ European Summer Meeting of the Association for Symbolic Logic ⋮ European Summer Meeting of the Association for Symbolic Logic ⋮ On Diophantine equations solvable in models of open induction ⋮ Real closures of models of weak arithmetic ⋮ Prime numbers and factorization in IE₁ and weaker systems ⋮ Improved bounds on the weak pigeonhole principle and infinitely many primes from weaker axioms ⋮ Combinatorial principles in elementary number theory ⋮ Independence results for variants of sharply bounded induction ⋮ 2008 European Summer Meeting of the Association for Symbolic Logic. Logic Colloquium '08 ⋮ Factorization in generalized power series ⋮ Non-standard finite fields over \(I\Delta_0+\Omega_1\) ⋮ A recursive nonstandard model of normal open induction ⋮ Quadratic forms in normal open induction

Cites Work

• On the scheme of induction for bounded arithmetic formulas
• Open induction and the true theory of rationals
• A Linearly Ordered Ring whose Theory Admits Elimination of Quantifiers is a Real Closed Field
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