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Nice local-global fields. I

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Abstract

The class NLGF of nice local-global fields and its three subclasses are introduced. The classes are stated to be recursively axiomatizable, and we establish a criterion of being elementarily embeddable for fields in mN LGF, fNLGF, and uNLGF. As a consequence, an elementary theory for the field of totally M-adic numbers is proved decidable for any finite set M of primes.

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Authors
  1. Yu. L. Ershov
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Additional information

Translated fromAlgebra i Logika, Vol. 35, No. 4, pp. 411–423, July–August, 1996.

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Ershov, Y.L. Nice local-global fields. I. Algebr Logic 35, 229–235 (1996). https://doi.org/10.1007/BF02367024

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  • DOI: https://doi.org/10.1007/BF02367024

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