Model Theory: Geometrical and Set-Theoretic Aspects and Prospects

DOI10.2178/bsl/1052669289zbMath1067.03044OpenAlexW2113125386MaRDI QIDQ4650297

Angus J. Macintyre

Publication date: 9 February 2005

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

Full work available at URL: https://projecteuclid.org/euclid.bsl/1052669289

zbMATH Keywords

model theorydefinabilitygeometric model theory

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) History of mathematical logic and foundations (03-03) Future perspectives in mathematics (01A67) Model theory (03Cxx)

Related Items (5)

Partial algebras, meaning categories and algebraization ⋮ Model-theory of vector-spaces over unspecified fields ⋮ Logic for physical space. From antiquity to present day ⋮ Algebraic cycles from a computational point of view ⋮ SPACES OF TYPES IN POSITIVE MODEL THEORY

Cites Work

• \(p\)-adic and real subanalytic sets
• Polynomial bounds for VC dimension of sigmoidal and general Pfaffian neural networks
• Galois stratification over Frobenius fields
• \(\aleph _ 0\)-categorical, \(\aleph _ 0\)-stable structures
• The elementary theory of restricted analytic fields with exponentiation
• Arithmetic analogues of derivations
• Generic automorphisms of fields
• Geometric categories and o-minimal structures
• A theorem of the complement and some new o-minimal structures
• The elementary theory of finite fields
• Definable sets, motives and 𝑝-adic integrals
• Model theory of difference fields
• Zariski geometries
• The Mordell-Lang conjecture for function fields
• Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function
• Logarithmic-exponential series
• The Manin-Mumford conjecture and the model theory of difference fields

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