Quantifier elimination for algebraic $D$-groups

DOI10.1090/S0002-9947-05-03820-1zbMath1075.03014OpenAlexW2087623002MaRDI QIDQ5694977

Piotr Kowalski, Anand Pillay

Publication date: 6 October 2005

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-05-03820-1

zbMATH Keywords

quantifier eliminationfirst-order structurealgebraic \(D\)-group

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Differential algebra (12H05) Model theory of fields (12L12) Quantifier elimination, model completeness, and related topics (03C10)

Related Items (13)

Ample thoughts ⋮ \(D\)-groups and the Dixmier-Moeglin equivalence ⋮ SEMIABELIAN VARIETIES OVER SEPARABLY CLOSED FIELDS, MAXIMAL DIVISIBLE SUBGROUPS, AND EXACT SEQUENCES ⋮ Algebraization, transcendence, and \(D\)-group schemes ⋮ A (possibly new) structure without the canonical base property ⋮ On the Dixmier-Moeglin equivalence for Poisson-Hopf algebras ⋮ CONSTRUCTING TYPES IN DIFFERENTIALLY CLOSED FIELDS THAT ARE ANALYSABLE IN THE CONSTANTS ⋮ A Lindemann-Weierstrass theorem for semi-abelian varieties over function fields ⋮ On parameterized differential Galois extensions ⋮ On algebraic 𝜎-groups ⋮ When any three solutions are independent ⋮ Differential Galois cohomology and parameterized Picard–Vessiot extensions ⋮ ADDITIVE COVERS AND THE CANONICAL BASE PROPERTY

Cites Work

• Geometrical model theory
• Differential algebraic groups of finite dimension
• A note on the axioms for differentially closed fields of characteristic zero
• Some foundational questions concerning differential algebraic groups
• Jet spaces of varieties over differential and difference fields
• A note on canonical bases and one-based types in supersimple theories
• Mordell–Lang conjecture for function fields in characteristic zero, revisited
• Model-theoretic consequences of a theorem of Campana and Fujiki
• The Mordell-Lang conjecture for function fields
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