Hilbert's tenth problem over function fields of positive characteristic not containing the algebraic closure of a finite field

DOI10.4171/JEMS/714zbMath1416.11171arXiv1306.2669MaRDI QIDQ2359446

Kirsten Eisenträger, Alexandra Shlapentokh

Publication date: 28 June 2017

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.2669

zbMATH Keywords

undecidabilityHilbert's tenth problem

Mathematics Subject Classification ID

Decidability (number-theoretic aspects) (11U05) Undecidability and degrees of sets of sentences (03D35)

Related Items (2)

As easy as $\mathbb {Q}$: Hilbert’s Tenth Problem for subrings of the rationals and number fields ⋮ Definability of Frobenius orbits and a result on rational distance sets

Cites Work

• Hilbert's tenth problem for fields of rational functions over finite fields
• The decision problem for exponential diophantine equations
• Diophantine unsolvability for function fields over certain infinite fields of characteristic \(p\)
• Hilbert's tenth problem for algebraic function fields over infinite fields of constants of positive characteristic
• Hilbert's tenth problem for function fields of varieties over algebraically closed fields of positive characteristic
• Hilbert's tenth problem for algebraic function fields of characteristic 2.
• Diophantine undecidability over algebraic function fields over finite fields of constants
• Uniform existential interpretation of arithmetic in rings of functions of positive characteristic
• Undecidable theories
• Undecidability in Function Fields of Positive Characteristic
• An Undecidability Result for Power Series Rings of Positive Characteristic. II
• Hilbert's Tenth Problem for Rational Function Fields in Characteristic 2
• Definability and decision problems in arithmetic
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