Dp-Minimality: Basic Facts and Examples

Notre Dame Journal of Formal Logic 52 (3):267-288 (2011)
  Copy   BIBTEX

Abstract

We study the notion of dp-minimality, beginning by providing several essential facts about dp-minimality, establishing several equivalent definitions for dp-minimality, and comparing dp-minimality to other minimality notions. The majority of the rest of the paper is dedicated to examples. We establish via a simple proof that any weakly o-minimal theory is dp-minimal and then give an example of a weakly o-minimal group not obtained by adding traces of externally definable sets. Next we give an example of a divisible ordered Abelian group which is dp-minimal and not weakly o-minimal. Finally we establish that the field of p -adic numbers is dp-minimal

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 74,509

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Quasi-o-Minimal Structures.Oleg Belegradek, Ya'acov Peterzil & Frank Wagner - 2000 - Journal of Symbolic Logic 65 (3):1115-1132.
Weakly o-Minimal Structures and Some of Their Properties.B. Sh Kulpeshov - 1998 - Journal of Symbolic Logic 63 (4):1511-1528.
Foundationalism.Daniel Howard-Snyder - 2012 - In Andrew Cullison (ed.), The Continuum Companion to Epistemology. Continuum. pp. 37.
What is o-Minimality?Harvey M. Friedman - 2008 - Annals of Pure and Applied Logic 156 (1):59-67.
Five Faces of Minimality.David Makinson - 1993 - Studia Logica 52 (3):339 - 379.
The Ontological Status of Minimal Entities.Luca Moretti - 2008 - Philosophical Studies 141 (1):97 - 114.
Minimality in the â–µ13-Degrees.Philip Welch - 1987 - Journal of Symbolic Logic 52 (4):908 - 915.

Analytics

Added to PP
2011-07-29

Downloads
24 (#477,320)

6 months
1 (#417,896)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Theories Without the Tree Property of the Second Kind.Artem Chernikov - 2014 - Annals of Pure and Applied Logic 165 (2):695-723.
Distal and Non-Distal NIP Theories.Pierre Simon - 2013 - Annals of Pure and Applied Logic 164 (3):294-318.
The Canonical Topology on Dp-Minimal Fields.Will Johnson - 2018 - Journal of Mathematical Logic 18 (2):1850007.

View all 19 citations / Add more citations

References found in this work

Generic Structures and Simple Theories.Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):71-92.
A Geometric Introduction to Forking and Thorn-Forking.Hans Adler - 2009 - Journal of Mathematical Logic 9 (1):1-20.
On Dp-Minimal Ordered Structures.Pierre Simon - 2011 - Journal of Symbolic Logic 76 (2):448 - 460.
Real Closed Rings II. Model Theory.Gregory Cherlin & Max A. Dickmann - 1983 - Annals of Pure and Applied Logic 25 (3):213-231.
A Version of o-Minimality for the P-Adics.Deirdre Haskell & Dugald Macpherson - 1997 - Journal of Symbolic Logic 62 (4):1075-1092.

View all 12 references / Add more references