Diophantine undecidability of \({\mathbb{C}{}}(t_ 1,t_ 2)\)

DOI10.1016/S0021-8693(05)80047-XzbMath0754.11039MaRDI QIDQ1194191

Kim Hang Kim, Fred W. Roush

Publication date: 27 September 1992

Published in: Journal of Algebra (Search for Journal in Brave)

zbMATH Keywords

undecidabilitycomplex function fieldDiophantine theory

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Decidability (number-theoretic aspects) (11U05) Decidability of theories and sets of sentences (03B25) Diophantine equations (11D99)

Related Items

Undecidable existential theories of polynomial rings and function fields ⋮ Automorphisms mapping a point into a subvariety ⋮ The work of Kim and Roush on questions of decidability in algebra and number theory ⋮ The publications of Ki Hang Kim ⋮ Extensions of Hilbert's tenth problem ⋮ Hilbert's Tenth problem for function fields of varieties over number fields and \(p\)-adic fields ⋮ Diophantine undecidability for some holomorphy rings of algebraic functions of characteristic 0. ⋮ The logic of pseudo-\(S\)-integers ⋮ Endomorphisms of elliptic curves and undecidability in function fields of positive characteristic. ⋮ Hilbert's tenth problem for rings of rational functions ⋮ Diophantine undecidability for some function fields of infinite transcendence degree and positive characteristic ⋮ Diophantine unsolvability for function fields over certain infinite fields of characteristic \(p\) ⋮ Hilbert's tenth problem for function fields of varieties over algebraically closed fields of positive characteristic ⋮ Diophantine undecidability of holomorphy rings of function fields of characteristic 0 ⋮ Integrality at a prime for global fields and the perfect closure of global fields of characteristic \(p > 2\) ⋮ DIOPHANTINE DEFINABILITY OVER HOLOMORPHY RINGS OF ALGEBRAIC FUNCTION FIELDS WITH INFINITE NUMBER OF PRIMES ALLOWED AS POLES ⋮ On Dipphantine definability and decidability in some rings of algebraic functions of characteristic 0

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