The algebraic numbers definable in various exponential fields

DOI10.1017/S1474748012000047zbMath1270.03057arXiv1101.4224OpenAlexW2161822986MaRDI QIDQ3167453

Alf Onshuus, Jonathan Kirby, Angus J. Macintyre

Publication date: 2 November 2012

Published in: Journal of the Institute of Mathematics of Jussieu (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.4224

zbMATH Keywords

Schanuel conjecturecomplex exponential fieldZilber models

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Model theory (number-theoretic aspects) (11U09) Model theory of fields (12L12) Categoricity and completeness of theories (03C35)

Related Items (5)

Turing meets Schanuel ⋮ COMPARING AND ZILBER’S EXPONENTIAL FIELDS: ZERO SETS OF EXPONENTIAL POLYNOMIALS ⋮ Generic solutions of equations with iterated exponentials ⋮ Involutions on Zilber fields ⋮ From Schanuel's conjecture to Shapiro's conjecture

Cites Work

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• Pseudo-exponentiation on algebraically closed fields of characteristic zero
• Fields of surreal numbers and exponentiation
• Exponential algebraicity in exponential fields
• A remark on Zilber's pseudoexponentiation
• On quasiminimal excellent classes
• Logarithmic-Exponential Power Series
• The removal of $\pi $ from some undecidable problems involving elementary functions
• Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function

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