Journal of Symbolic Logic

Existential definability with bounds on archimedean valuations

Alexandra Shlapentokh

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Abstract

We show that a solution to Hilbert’s Tenth Problem in the rings of algebraic integers and bigger subrings of number fields where it is currently not known, is equivalent to a problem of bounding archimedean valuations over non-real number fields.

Article information

Source
J. Symbolic Logic, Volume 68, Issue 3 (2003), 860- 878.

Dates
First available in Project Euclid: 17 July 2003

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1058448445

Digital Object Identifier
doi:10.2178/jsl/1058448445

Mathematical Reviews number (MathSciNet)
MR2004g:11118

Zentralblatt MATH identifier
1068.03011

Citation

Shlapentokh, Alexandra. Existential definability with bounds on archimedean valuations. J. Symbolic Logic 68 (2003), no. 3, 860-- 878. doi:10.2178/jsl/1058448445. https://projecteuclid.org/euclid.jsl/1058448445


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