Undecidability and definability for the theory of global fields

Rumely, R. S.

doi:10.1090/S0002-9947-1980-0583852-6

Undecidability and definability for the theory of global fields
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by R. S. Rumely PDF

Trans. Amer. Math. Soc. 262 (1980), 195-217 Request permission

Abstract:

We prove that the theory of global fields is essentially undecidable, using predicates based on Hasse’s Norm Theorem to define valuations. Polynomial rings or the natural numbers are uniformly defined in all global fields, as well as Gödel functions encoding finite sequences of elements.

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