On the finiteness theorem of Siegel and Mahler concerning diophantine equations

DOI10.1016/0022-314X(75)90013-XzbMath0299.12107MaRDI QIDQ1214965

Peter Roquette, Abraham Robinson

Publication date: 1975

Published in: Journal of Number Theory (Search for Journal in Brave)

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Nonstandard arithmetic (number-theoretic aspects) (11U10) Nonstandard models (03H99) Nonstandard arithmetic and field theory (12L15)

Related Items (15)

Arithmetically independent integers and values of rational functions ⋮ Étale Galois covers of affine smooth curves. The geometric case of a conjecture of Shafarevich. On Abhyankar's conjecture ⋮ Hilbert irreducibility sequences and nonstandard arithmetic ⋮ Numbers and models, standard and nonstandard ⋮ Cyclic isogenies and nonstandard arithmetic ⋮ Nonstandard Arithmetic of Polynomial Rings ⋮ Approximation properties and existential completeness for ring morphisms ⋮ Nonstandard arithmetic of iterated polynomials ⋮ The Mordell-Lang conjecture for function fields ⋮ Abraham Robinson, 1918-1974 ⋮ Les nombres transcendants ⋮ Abraham Robinson 1918-1974 ⋮ Seshadri constants, Diophantine approximation, and Roth's theorem for arbitrary varieties ⋮ Nonstandard arithmetic of Hilbert subsets ⋮ Applied model theory and metamathematics. An Abraham Robinson memorial problem list

Cites Work

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• Nonstandard points on algebraic curves
• Bemerkungen zur Theorie der formal \(p\)-adischen Körper
• A remark on Siegel's theorem on algebraic curves
• The p ‐adic generalization of the Thue‐Siegel‐Roth theorem
• Rational points on curves of genus greater than 1.
• Nonstandard arithmetic
• Arithmetischer Beweis der Riemannschen Vermutung in Kongruenzfunktionenkörpern beliebigen Geschlechts.
• Axiomatic characterization of fields by the product formula for valuations
• Rational approximations to algebraic numbers
• Rational approximations to algebraic numbers
• Non-standard analysis
• Arithmetic on algebraic varieties

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