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Undecidability and definability for the theory of global fields


Author: R. S. Rumely
Journal: Trans. Amer. Math. Soc. 262 (1980), 195-217
MSC: Primary 03D35; Secondary 10N05, 12L05
DOI: https://doi.org/10.1090/S0002-9947-1980-0583852-6
MathSciNet review: 583852
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1980-0583852-6
Keywords: Undecidability, definability, global fields, function fields, number fields, Hasse Principle, valuations
Article copyright: © Copyright 1980 American Mathematical Society

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