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- W2109200492 abstract "Abstract Let K be a function field of one variable over a constant field C of finite transcendence degree over ℂ. Let M/K be a finite extension and let W be a set of primes of K such that all but finitely many primes of W do not split in the extension M/K . Then there exists a set W′ of K -primes such that Hilbert's Tenth Problem is not decidable over O K,W′ = { x ϵ K ∣ord þ x ≥ 0, ∀þ ∉ W′ }, and the set ( W ′ ∖ W )∪{ W ∖ W ′) is finite. Let K be a function field of one variable over a constant field C finitely generated over ℚ. Let M/K be a finite extension and let W be a set of primes of K such that all but finitely many primes of W do not split in the extension M/K and the degree of all the primes in W is bounded by b ϵ ℕ. Then there exists a set W ′ of K -primes such that ℤ has a Diophantine definition over O K, W ′ , and the set ( W ′ ∖ W )∪( W ∖ W ′) is finite." @default.
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- W2109200492 date "2002-06-01" @default.
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- W2109200492 title "On Dipphantine definability and decidability in some rings of algebraic functions of characteristic 0" @default.
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