Definable sets in ordered structures. II

Knight, Julia F.; Pillay, Anand; Steinhorn, Charles

doi:10.1090/S0002-9947-1986-0833698-1

Definable sets in ordered structures. II
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by Julia F. Knight, Anand Pillay and Charles Steinhorn PDF

Trans. Amer. Math. Soc. 295 (1986), 593-605 Request permission

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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