Describing groups

Bulletin of Symbolic Logic 13 (3):305-339 (2007)
Abstract
Two ways of describing a group are considered. 1. A group is finite-automaton presentable if its elements can be represented by strings over a finite alphabet, in such a way that the set of representing strings and the group operation can be recognized by finite automata. 2. An infinite f.g. group is quasi-finitely axiomatizable if there is a description consisting of a single first-order sentence, together with the information that the group is finitely generated. In the first part of the paper we survey examples of FA-presentable groups, but also discuss theorems restricting this class. In the second part, we give examples of quasi-finitely axiomatizable groups, consider the algebraic content of the notion, and compare it to the notion of a group which is a prime model. We also show that if a structure is bi-interpretable in parameters with the ring of integers, then it is prime and quasi-finitely axiomatizable
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
 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
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 10,768
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Citations of this work BETA
Similar books and articles
Frank O. Wagner (1991). Small Stable Groups and Generics. Journal of Symbolic Logic 56 (3):1026-1037.
Analytics

Monthly downloads

Added to index

2010-08-30

Total downloads

2 ( #345,621 of 1,099,016 )

Recent downloads (6 months)

1 ( #287,293 of 1,099,016 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.