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Interpreting structures of finite Morley Rank in strongly minimal sets

Abstract:

We show that any structure of finite Morley Rank having the definable multiplicity property (DMP) has a rank and multiplicity preserving interpretation in a strongly minimal set. In particular, every totally categorical theory admits such an interpretation. We also show that a slightly weaker version of the DMP is necessary for a structure of finite rank to have a strongly minimal expansion. We conclude by constructing an almost strongly minimal set which does not have the DMP in any rank ...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.apal.2006.10.002

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Elsevier
Journal:
Annals of Pure and Applied Logic More from this journal
Volume:
145
Issue:
1
Pages:
96-114
Publication date:
2007-01-01
DOI:
ISSN:
0168-0072
Language:
English
Keywords:
UUID:
uuid:91659966-7e75-4fdb-9f7a-e8e8f9422fcf
Local pid:
pubs:27187
Source identifiers:
27187
Deposit date:
2012-12-19

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