On ℵ0-categorical weakly o-minimal structures

✍ Scribed by B. Herwig; H.D. Macpherson; G. Martin; A. Nurtazin; J.K. Truss

• Book ID: 104307481
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 288 KB
• Volume: 101
• Category: Article
• ISSN: 0168-0072
• DOI: 10.1016/s0168-0072(99)00029-9

✦ Synopsis

ℵ 0-categorical o-minimal structures were completely described by Pillay and Steinhorn (Trans. Amer. Math. Soc. 295 (1986) , 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 ℵ 0-categorical weakly o-minimal set may carry, and ÿnd 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 classiÿed up to binary structure; the structure is 2-indiscernible, classiÿed up to ternary structure; the structure is 3-indiscernible, in which case we show that it is k-indiscernible for every ÿnite k. We also make some remarks about the possible structures of higher arities which an ℵ 0-categorical weakly o-minimal structure may carry.