Defining Integers-Reference-Cited by-同舟云学术

Defining Integers

Published:2011-06 Issue:2 Volume:17 Page:230-251
ISSN:1079-8986
Container-title:The Bulletin of Symbolic Logic
language:en
Short-container-title:Bull. symb. log

Author:

Shlapentokh Alexandra

Abstract

AbstractThis paper surveys the recent developments in the area that grew out of attempts to solve an analog of Hilbert's Tenth Problem for the field of rational numbers and the rings of integers of number fields. It is based on a plenary talk the author gave at the annual North American meeting of ASL at the University of Notre Dame in May of 2009.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Reference36 articles.

1. Hilbert's Tenth Problem

2. Diophantine Sets over Some Rings of Algebraic Integers

3. Diophantine Definability and Decidability in Large Subrings of Totally Real Number Fields and Their Totally Complex Extensions of Degree 2

4. Topology of Diophantine sets: remarks on Mazur’s conjectures

5. Ranks of twists of elliptic curves and Hilbert’s tenth problem

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