Definability and definable groups in simple theories

Journal of Symbolic Logic 63 (3):788-796 (1998)
  Copy   BIBTEX

Abstract

We continue the study of simple theories begun in [3] and [5]. We first find the right analogue of definability of types. We then develop the theory of generic types and stabilizers for groups definable in simple theories. The general ideology is that the role of formulas (or definability) in stable theories is replaced by partial types (or ∞-definability) in simple theories

Categories

Keywords

Reprint years

DOI

10.2307/2586712

Other Versions

reprint Pillay, Anand (1999) "Definability and Definable Groups in Simple Theories". Journal of Symbolic Logic 64(3):788-796

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 107,286

External links

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

Through your library

My notes

Similar books and articles

On uniform definability of types over finite sets.Vincent Guingona - 2012 - Journal of Symbolic Logic 77 (2):499-514.
Definability in number fields.S. P. Tung - 1987 - Journal of Symbolic Logic 52 (1):152-155.
Stable Definability and Generic Relations.Byunghan Kim & Rahim Moosa - 2007 - Journal of Symbolic Logic 72 (4):1163 - 1176.
Mutual definability does not imply definitional equivalence, a simple example.Hajnal Andréka, Judit X. Madarász & István Németi - 2005 - Mathematical Logic Quarterly 51 (6):591-597.
On definability of types and relative stability.Viktor Verbovskiy - 2019 - Mathematical Logic Quarterly 65 (3):332-346.
On forking and definability of types in some dp-minimal theories.Pierre Simon & Sergei Starchenko - 2014 - Journal of Symbolic Logic 79 (4):1020-1024.
The number of types in simple theories.Enrique Casanovas - 1999 - Annals of Pure and Applied Logic 98 (1-3):69-86.
Unidimensional theories are superstable.Ehud Hrushovski - 1990 - Annals of Pure and Applied Logic 50 (2):117-138.
Unidimensional theories are superstable.Katsuya Eda - 1990 - Annals of Pure and Applied Logic 50 (2):117-137.
Definability in low simple theories.Ziv Shami - 2000 - Journal of Symbolic Logic 65 (4):1481-1490.

Analytics

Added to PP
2009-01-28

Downloads
46 (#560,688)

6 months
14 (#278,392)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Simplicity in compact abstract theories.Itay Ben-Yaacov - 2003 - Journal of Mathematical Logic 3 (02):163-191.
Pseudofinite structures and simplicity.Darío García, Dugald Macpherson & Charles Steinhorn - 2015 - Journal of Mathematical Logic 15 (1):1550002.
On Rank Not Only in Nsop $_1$ Theories.Jan Dobrowolski & Daniel Max Hoffmann - 2024 - Journal of Symbolic Logic 89 (4):1669-1702.
From stability to simplicity.Byunghan Kim & Anand Pillay - 1998 - Bulletin of Symbolic Logic 4 (1):17-36.
Hyperdefinable groups in simple theories.Frank Wagner - 2001 - Journal of Mathematical Logic 1 (01):125-172.

View all 8 citations / Add more citations

References found in this work

Simple theories.Byunghan Kim & Anand Pillay - 1997 - Annals of Pure and Applied Logic 88 (2-3):149-164.
Simple unstable theories.Saharon Shelah - 1980 - Annals of Mathematical Logic 19 (3):177.

Add more references