312 research outputs found
Stable embeddedness and NIP
We give sufficient conditions for a predicate P in a complete theory T to be
stably embedded: P with its induced 0-definable structure has "finite rank", P
has NIP in T and P is 1-stably embedded. This generalizes recent work by Hasson
and Onshuus in the case where P is o-minimal in T.Comment: 10 page
Connected components of definable groups and o-minimality I
We give examples of groups G such that G^00 is different from G^000. We also
prove that for groups G definable in an o-minimal structure, G has a "bounded
orbit" iff G is definably amenable. These results answer questions of
Gismatullin, Newelski, Petrykovski. The examples also give new non G-compact
first order theories.Comment: 26 pages. This paper corrects the paper "Groups definable in
o-minimal structures: structure theorem, G^000, definable amenability, and
bounded orbits" by the first author which was posted in December
(1012.4540v1) and later withdraw
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