On ℵ0-categorical weakly o-minimal structures Original Research Article

View the MathML source-categorical o-minimal structures were completely described by Pillay and Steinhorn (Trans. Amer. Math. Soc. 295 (1986) 565–592), 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 View the MathML source-categorical weaklyo-minimal set may carry, and find 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 classified up to binary structure; the structure is 2-indiscernible, classified up to ternary structure; the structure is 3-indiscernible, in which case we show that it is k-indiscernible for every finite k. We also make some remarks about the possible structures of higher arities which an View the MathML source-categorical weakly o-minimal structure may carry.