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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Definable sets in ordered structures. II


Authors: Julia F. Knight, Anand Pillay and Charles Steinhorn
Journal: Trans. Amer. Math. Soc. 295 (1986), 593-605
MSC: Primary 03C45; Secondary 03C40, 03C50, 06F99
MathSciNet review: 833698
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Abstract: It is proved that any 0-minimal structure $ M$ (in which the underlying order is dense) is strongly 0-minimal (namely, every $ N$ elementarily equivalent to $ M$ is 0-minimal). It is simultaneously proved that if $ M$ is 0-minimal, then every definable set of $ n$-tuples of $ M$ has finitely many "definably connected components."


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0833698-1
PII: S 0002-9947(1986)0833698-1
Keywords: 0-minimal, definably connected, cell
Article copyright: © Copyright 1986 American Mathematical Society