Some model theory for almost real closed fields

DOI10.2307/2275808zbMath0874.03045OpenAlexW2138440159MaRDI QIDQ3128465

Rafel Farré, Françoise Delon

Publication date: 6 November 1997

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

Full work available at URL: https://doi.org/10.2307/2275808

zbMATH Keywords

elementary equivalencereal closed fieldHenselian valuationreal valuation ringselementary inclusionfirst-order definable convex subgroupstheories of ordered Abelian groups

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Decidability of theories and sets of sentences (03B25) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20) Model theory of fields (12L12) Valued fields (12J10)

Related Items

Ordered fields dense in their real closure and definable convex valuations ⋮ Distality in valued fields and related structures ⋮ Strongly NIP almost real closed fields ⋮ DEFINABILITY OF HENSELIAN VALUATIONS BY CONDITIONS ON THE VALUE GROUP ⋮ Definable valuations on ordered fields ⋮ Definable V-topologies, Henselianity and NIP ⋮ Recent progress on definability of Henselian valuations ⋮ Central Extensions of n-Ordered Division Rings ⋮ Strongly dependent ordered abelian groups and Henselian fields ⋮ Valuation fans and residually closed Henselian fields

Cites Work

• Unnamed Item
• Lectures on formally real fields
• Chains of higher level orderings
• Elementary properties of ordered abelian groups