dc.contributor.author |
Nies, Andre |
en |
dc.date.accessioned |
2011-11-30T19:07:34Z |
en |
dc.date.issued |
2007 |
en |
dc.identifier.citation |
Bulletin of Symbolic Logic 13:305-339 2007 |
en |
dc.identifier.issn |
1079-8986 |
en |
dc.identifier.uri |
http://hdl.handle.net/2292/9656 |
en |
dc.description.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. |
en |
dc.publisher |
Association for Symbolic Logic |
en |
dc.relation.ispartofseries |
Bulletin of Symbolic Logic |
en |
dc.rights |
Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher.
http://www.sherpa.ac.uk/romeo/issn/1079-8986/ |
en |
dc.rights.uri |
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm |
en |
dc.title |
Describing Groups |
en |
dc.type |
Journal Article |
en |
dc.identifier.doi |
10.2178/bsl/1186666149 |
en |
pubs.begin-page |
305 |
en |
pubs.volume |
13 |
en |
dc.rights.holder |
Copyright: Association for Symbolic Logic |
en |
pubs.author-url |
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.bsl/1186666149 |
en |
pubs.end-page |
339 |
en |
dc.rights.accessrights |
http://purl.org/eprint/accessRights/RestrictedAccess |
en |
pubs.subtype |
Article |
en |
pubs.elements-id |
76433 |
en |
pubs.org-id |
Science |
en |
pubs.org-id |
School of Computer Science |
en |
pubs.record-created-at-source-date |
2010-09-01 |
en |