Iteratively Changing the Heights of Automorphism Towers

Notre Dame Journal of Formal Logic 53 (2):155-174 (2012)
We extend the results of Hamkins and Thomas concerning the malleability of automorphism tower heights of groups by forcing. We show that any reasonable sequence of ordinals can be realized as the automorphism tower heights of a certain group in consecutive forcing extensions or ground models, as desired. For example, it is possible to increase the height of the automorphism tower by passing to a forcing extension, then increase it further by passing to a ground model, and then decrease it by passing to a further forcing extension, and so on, transfinitely. We make sense of the limit models occurring in such a sequence of models. At limit stages, the automorphism tower height will always be 1
Keywords automorphism tower   forcing   maximality principle
Categories (categorize this paper)
DOI 10.1215/00294527-1715662
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 29,511
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
A Simple Maximality Principle.Joel David Hamkins - 2003 - Journal of Symbolic Logic 68 (2):527-550.
On Automorphism Groups of Countable Structures.Su Gao - 1998 - Journal of Symbolic Logic 63 (3):891-896.
Automorphism Groups of Trivial Strongly Minimal Structures.Thomas Blossier - 2003 - Journal of Symbolic Logic 68 (2):644-668.
Philosophy for the Eye.Roy Sorensen - 2008 - The Philosophers' Magazine 42 (42):31-39.
Model Companions of Theories with an Automorphism.Hirotaka Kikyo - 2000 - Journal of Symbolic Logic 65 (3):1215-1222.
Large Cardinals and Large Dilators.Andy Lewis - 1998 - Journal of Symbolic Logic 63 (4):1496-1510.
The Consistency Strength of $\Mathrm{MP_{CCC}}(\Mathbb{R})$.George Leibman - 2010 - Notre Dame Journal of Formal Logic 51 (2):181-193.
Laver Indestructibility and the Class of Compact Cardinals.Arthur W. Apter - 1998 - Journal of Symbolic Logic 63 (1):149-157.
Automorphism Properties of Stationary Logic.Martin Otto - 1992 - Journal of Symbolic Logic 57 (1):231-237.
Automorphism Groups of Models of Peano Arithmetic.James H. Schmerl - 2002 - Journal of Symbolic Logic 67 (4):1249-1264.
Automorphism Groups of Arithmetically Saturated Models.Ermek S. Nurkhaidarov - 2006 - Journal of Symbolic Logic 71 (1):203 - 216.
Solovay Models and Forcing Extensions.Joan Bagaria & Roger Bosch - 2004 - Journal of Symbolic Logic 69 (3):742-766.
Added to PP index

Total downloads
9 ( #468,916 of 2,180,707 )

Recent downloads (6 months)
1 ( #301,383 of 2,180,707 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature

There  are no threads in this forum
Nothing in this forum yet.

Other forums