Set theory generated by Abelian group theory

Bulletin of Symbolic Logic 3 (1):1-16 (1997)
  Copy   BIBTEX

Abstract

Introduction. This survey is intended to introduce to logicians some notions, methods and theorems in set theory which arose—largely through the work of Saharon Shelah—out of attempts to solve problems in abelian group theory, principally the Whitehead problem and the closely related problem of the existence of almost free abelian groups. While Shelah's first independence result regarding the Whitehead problem used established set-theoretical methods, his later work required new ideas; it is on these that we focus. We emphasize the nature of the new ideas and the historical context in which they arose, and we do not attempt to give precise technical definitions in all cases, nor to include a comprehensive survey of the algebraic results.In fact, very little algebraic background is needed beyond the definitions of group and group homomorphism. Unless otherwise specified, we will use the word “group” to refer to an abelian group, that is, the group operation is commutative. The group operation will be denoted by +, the identity element by 0, and the inverse of a by −a. We shall use na as an abbreviation for a + a + … + a [n times] if n is positive, and na = if n is negative.

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 102,546

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

On properties of (weakly) small groups.Cédric Milliet - 2012 - Journal of Symbolic Logic 77 (1):94-110.
Polynomial-time abelian groups.Douglas Cenzer & Jeffrey Remmel - 1992 - Annals of Pure and Applied Logic 56 (1-3):313-363.
Finite automata presentable Abelian groups.André Nies & Pavel Semukhin - 2010 - Annals of Pure and Applied Logic 161 (3):458-467.
On superstable CSA-groups.Abderezak Houcine - 2008 - Annals of Pure and Applied Logic 154 (1):1-7.
On superstable CSA-groups.Abderezak Ould Houcine - 2008 - Annals of Pure and Applied Logic 154 (1):1-7.
Axiomatization of abelian-by- G groups for a finite group G.Francis Oger - 2001 - Archive for Mathematical Logic 40 (7):515-521.
Interpretable groups in Mann pairs.Haydar Göral - 2018 - Archive for Mathematical Logic 57 (3-4):203-237.
From "metabelian q-vector spaces" to new ω-stable groups.Olivier Chapuis - 1996 - Bulletin of Symbolic Logic 2 (1):84-93.

Analytics

Added to PP
2009-01-28

Downloads
51 (#439,692)

6 months
10 (#364,029)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

Multiple Forcing.T. Jech - 1989 - Journal of Symbolic Logic 54 (3):1112-1113.
Incompactness in regular cardinals.Saharon Shelah - 1985 - Notre Dame Journal of Formal Logic 26 (3):195-228.
Categoricity results for L∞κ.Paul C. Eklof & Alan H. Mekler - 1988 - Annals of Pure and Applied Logic 37 (1):81-99.

Add more references