Logarithmic-exponential series

DOI10.1016/S0168-0072(01)00035-5zbMath0998.12014MaRDI QIDQ5942884

Angus J. Macintyre, L. P. D. van den Dries, David Marker

Publication date: 11 September 2001

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

zbMATH Keywords

Hardy fieldlogarithmic-exponential seriestransseries

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Differential algebra (12H05) Ordered fields (12J15) Model theory of fields (12L12)

Related Items (34)

Book review of: M. Aschenbrenner et al., Asymptotic differential algebra and model theory of transseries ⋮ A note on Schanuel's conjectures for exponential logarithmic power series fields ⋮ Normal forms and embeddings for power-log transseries ⋮ The asymptotic couple of the field of logarithmic transseries ⋮ ASYMPTOTIC ANALYSIS OF SKOLEM’S EXPONENTIAL FUNCTIONS ⋮ Ilyashenko algebras based on transserial asymptotic expansions ⋮ Toward a model theory for transseries ⋮ Liouville closed \(H_T\)-fields ⋮ Valued fields with contractive automorphism and Kaplansky fields ⋮ \(T\)-convex \(T\)-differential fields and their immediate extensions ⋮ Taming the landscape of effective theories ⋮ Real closed valued fields with analytic structure ⋮ Meta-expansion of transseries ⋮ Normalization of strongly hyperbolic logarithmic transseries and complex Dulac germs ⋮ Transseries and Todorov-Vernaeve's asymptotic fields ⋮ The Fatou coordinate for parabolic Dulac germs ⋮ Tubular neighborhoods of orbits of power-logarithmic germs ⋮ Closed asymptotic couples ⋮ Analytic continuations of log-exp-analytic germs ⋮ Dimension in the realm of transseries ⋮ Surreal numbers with derivation, Hardy fields and transseries: a survey ⋮ On the value group of the transseries ⋮ Transseries as germs of surreal functions ⋮ Model Theory: Geometrical and Set-Theoretic Aspects and Prospects ⋮ The exponential-logarithmic equivalence classes of surreal numbers ⋮ Liouville closed \(H\)-fields ⋮ Maps on Ultrametric Spaces, Hensel's Lemma, and Differential Equations Over Valued Fields ⋮ Linearization of complex hyperbolic Dulac germs ⋮ Fractional iteration of series and transseries ⋮ \(\kappa\)-bounded exponential-logarithmic power series fields ⋮ Algebraic properties of rings of generalized power series ⋮ Normal forms of hyperbolic logarithmic transseries ⋮ Comparison of exponential-logarithmic and logarithmic-exponential series ⋮ Logarithms, constructible functions and integration on non-archimedean models of the theory of the real field with restricted analytic functions with value group of finite archimedean rank

Cites Work

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• The Rank of a Hardy Field
• Borel Orderings
• Convergent Series Expansions of a New Type for Exponential Functions
• The limit behaviour of exponential terms
• Growth Properties of Functions in Hardy Fields
• Solution d'un problème d'Erdős,Gillman etHenriksen et application a l'étude des homomorphismes de $$C$$ (K)(K)
• Exponentiation in power series fields
• Logarithmic-Exponential Power Series
• Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function
• On Ordered Division Rings

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