Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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
MathSciNet review: 583852
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 03D35, 10N05, 12L05

Retrieve articles in all journals with MSC: 03D35, 10N05, 12L05


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