Properties of forking in ω-free pseudo-algebraically closed fields

DOI10.2178/jsl/1190150143zbMath1032.03033OpenAlexW2045117194MaRDI QIDQ4779645

Zoé Chatzidakis

Publication date: 17 March 2004

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

Full work available at URL: https://doi.org/10.2178/jsl/1190150143

zbMATH Keywords

forkingpseudo-algebraically closed fieldsimple theory\(\omega\)-free field

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Classification theory, stability, and related concepts in model theory (03C45) Model theory of fields (12L12)

Related Items (18)

Pseudo real closed fields, pseudo \(p\)-adically closed fields and \(\mathrm{NTP}_{2}\) ⋮ On Kim-independence ⋮ Co-theory of sorted profinite groups for PAC structures ⋮ Kim-independence in positive logic ⋮ Notions around tree property 1 ⋮ THE ELEMENTARY THEORY OF LARGE FIELDS OF TOTALLY -ADIC NUMBERS ⋮ Perfect pseudo-algebraically closed fields are algebraically bounded. ⋮ Imaginaries, invariant types and pseudo \(p\)-adically closed fields ⋮ On Galois groups and PAC substructures ⋮ 2010 European Summer Meeting of the Association for Symbolic Logic. Logic Colloquium '10 ⋮ FORKING, IMAGINARIES, AND OTHER FEATURES OF ⋮ Generic expansions by a reduct ⋮ Amalgamation of types in pseudo-algebraically closed fields and applications ⋮ On PAC and bounded substructures of a stable structure ⋮ Independence over arbitrary sets in \(\mathrm{NSOP}_1\) theories ⋮ Quantifier elimination on some pseudo-algebraically closed valued fields ⋮ ELEMENTARY EQUIVALENCE THEOREM FOR PAC STRUCTURES ⋮ WEAK CANONICAL BASES IN NSOP THEORIES

Cites Work

• Dimension of definable sets, algebraic boundedness and Henselian fields
• Undecidability of regularly closed fields
• Embedding covers and the theory of Frobenius fields
• The elementary theory of algebraic fields of finite corank
• The elementary theory of \(\omega\)-free \(Ax\) fields
• Generic structures and simple theories
• Groups definable in local fields and pseudo-finite fields
• Simple theories
• Complete theories of algebraically closed fields with distinguished subfields
• The elementary theory of finite fields
• Decidability and undecidability theorems for PAC-fields
• Forking in Simple Unstable Theories

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