On ℵ0-categorical weakly o-minimal structures

Annals of Pure and Applied Logic 101 (1):65-93 (1999)
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Abstract

0-categorical o-minimal structures were completely described by Pillay and Steinhorn 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 0-categorical weakly o-minimal set may carry, and find that there are some rather more interesting 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 0-categorical weakly o-minimal structure may carry

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Citations of this work

Notes on Local o‐Minimality.Carlo Toffalori & Kathryn Vozoris - 2009 - Mathematical Logic Quarterly 55 (6):617-632.
Vaught's Conjecture for Quite o-Minimal Theories.B. Sh Kulpeshov & S. V. Sudoplatov - 2017 - Annals of Pure and Applied Logic 168 (1):129-149.
On o-Amorphous Sets.P. Creed & J. K. Truss - 2000 - Annals of Pure and Applied Logic 101 (2-3):185-226.

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References found in this work

Elimination of Quantifiers for Ordered Valuation Rings.M. A. Dickmann - 1987 - Journal of Symbolic Logic 52 (1):116-128.

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