On N0-Categorical Weakly o-Minimal Structures

@0-categorical o-minimal structures were completely described in 4], and are essentially built up from copies of the rationals as an ordered set by`cutting and copying'. Here we investigate the possible structures which an @0-categorical weakly o-minimal set may carry, and nd that there are some rather more interesting (and not o-minimal) examples. We show that even here the possibilities are limited. We subdivide our study into the following principal cases: the structure is 1-indiscernible, in which case all possibilities are classiied up to binary structure; the structure is 2-indiscernible, classiied up to ternary structure; the structure is 3-indiscernible, in which case we show that it is k-indiscernible for every nite k. We also make some remarks about the possible structures of higher arities which an @0-categorical weakly o-minimal structure may carry.