## Journal of Symbolic Logic

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

### Existential definability with bounds on archimedean valuations

#### 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