$\mathbb \{Q\}$ muni de l’arithmétique faible de Penzin est décidable

DOI10.1090/S0002-9939-97-03912-9zbMath0880.03019MaRDI QIDQ4372333

Françoise Delon

Publication date: 11 December 1997

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

decidability\(p\)-adic valuationfield of rational numbersPenzin arithmetic

Mathematics Subject Classification ID

Decidability and field theory (12L05) Model-theoretic algebra (03C60)

Related Items (4)

Equivalence elementaire et decidabilite pour des structures du type groupe agissant sur un groupe abelien ⋮ Un principe d'ax-kochen-ershov pour des structures intermédiates entre groupes et corps valués ⋮ A tetrachotomy for expansions of the real ordered additive group ⋮ Decidability questions for a ring of Laurent polynomials

Cites Work

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• Lokalinvariante Bewertungen. (Locally invariant valuations)
• The field of reals with a predicate for the powers of two
• Logic and \(p\)-recognizable sets of integers
• Solvability of the theory of integers with addition, order, and multiplication by an arbitrary number
• Une correspondance entre anneaux partiels et groupes
• Un principe d'ax-kochen-ershov pour des structures intermédiates entre groupes et corps valués
• Definability and decision problems in arithmetic
• Undecidable Rings
• Solution of a problem of Tarski

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