- New
-
Topics
- All Categories
- Metaphysics and Epistemology
- Value Theory
- Science, Logic, and Mathematics
- Science, Logic, and Mathematics
- Logic and Philosophy of Logic
- Philosophy of Biology
- Philosophy of Cognitive Science
- Philosophy of Computing and Information
- Philosophy of Mathematics
- Philosophy of Physical Science
- Philosophy of Social Science
- Philosophy of Probability
- General Philosophy of Science
- Philosophy of Science, Misc
- History of Western Philosophy
- Philosophical Traditions
- Philosophy, Misc
- Other Academic Areas
- Journals
- Submit material
- More
Diophantine undecidability in some rings of algebraic numbers of totally real infinite extensions of Q
Annals of Pure and Applied Logic 68 (3):299-325 (1994)
Abstract
This paper provides the first examples of rings of algebraic numbers containing the rings of algebraic integers of the infinite algebraic extensions of where Hilbert's Tenth Problem is undecidableAuthor's Profile
Other Versions
No versions found
My notes
Similar books and articles
Rings of algebraic numbers in infinite extensions of $${\mathbb {Q}}$$ and elliptic curves retaining their rank.Alexandra Shlapentokh - 2009 - Archive for Mathematical Logic 48 (1):77-114.
A Diophantine definition of rational integers over some rings of algebraic numbers.Alexandra Shlapentokh - 1992 - Notre Dame Journal of Formal Logic 33 (3):299-321.
First-order definitions of rational functions and S -integers over holomorphy rings of algebraic functions of characteristic 0.Alexandra Shlapentokh - 2005 - Annals of Pure and Applied Logic 136 (3):267-283.
Definability of the ring of integers in some infinite algebraic extensions of the rationals.Kenji Fukuzaki - 2012 - Mathematical Logic Quarterly 58 (4-5):317-332.
Existential definability with bounds on archimedean valuations.Alexandra Shlapentokh - 2003 - Journal of Symbolic Logic 68 (3):860-878.
Diophantine definability over non-finitely generated non-degenerate modules of algebraic extensions of ℚ.Alexandra Shlapentokh - 2001 - Archive for Mathematical Logic 40 (4):297-328.
The elementary theory of e-free PAC domains.Aharon Razon - 2000 - Annals of Pure and Applied Logic 103 (1-3):55-95.
The Undecidability of Algebraic Rings and Fields.Julia Robinson - 1964 - Journal of Symbolic Logic 29 (1):57-58.
Denseness results in the theory of algebraic fields.Sylvy Anscombe, Philip Dittmann & Arno Fehm - 2021 - Annals of Pure and Applied Logic 172 (8):102973.
Algebraic extensions in nonstandard models and Hilbert's irreducibility theorem.Masahiro Yasumoto - 1988 - Journal of Symbolic Logic 53 (2):470-480.
Analytics
Added to PP
2014-01-16
Downloads
31 (#727,171)
6 months
10 (#404,653)
2014-01-16
Downloads
31 (#727,171)
6 months
10 (#404,653)
Historical graph of downloads
Author's Profile
Citations of this work
Diophantine definability over non-finitely generated non-degenerate modules of algebraic extensions of ℚ.Alexandra Shlapentokh - 2001 - Archive for Mathematical Logic 40 (4):297-328.
Rings of algebraic numbers in infinite extensions of $${\mathbb {Q}}$$ and elliptic curves retaining their rank.Alexandra Shlapentokh - 2009 - Archive for Mathematical Logic 48 (1):77-114.
On Diophantine definability and decidability in some rings of algebraic functions of characteristic 0.Alexandra Shlapentokh - 2002 - Journal of Symbolic Logic 67 (2):759-786.
References found in this work
A Diophantine definition of rational integers over some rings of algebraic numbers.Alexandra Shlapentokh - 1992 - Notre Dame Journal of Formal Logic 33 (3):299-321.
PhilPapers logo by Andrea Andrews and Meghan Driscoll.
This site uses cookies and Google Analytics (see our terms & conditions for details regarding the privacy implications). Use of this site is subject to terms & conditions.
All rights reserved by The PhilPapers Foundation
Server: philpapers-web-667477cd97-wmc4m dc2