2007/04/29 by Hasson, Assaf, Onshuus, Alf
#03C45 #03C64 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.0704.3844
Let M be an o-minimal structure with elimination of imaginaries, N an unstable structure definable in M. Then there exists X, interpretable in N, such that X with all the structure induced from N is o-minimal. In particular X is linearly ordered. As part of the proof we show: Theorem 1: If the M-dimenson of N is 1 then any 1-N-type is either strongly stable or finite by o-minimal. Theorem 2: If N is N-minimal then it is 1-M-dimensional.