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  1. On variants of o-minimality.Dugald Macpherson & Charles Steinhorn - 1996 - Annals of Pure and Applied Logic 79 (2):165-209.
  • Weakly o-minimal structures and some of their properties.B. Sh Kulpeshov - 1998 - Journal of Symbolic Logic 63 (4):1511-1528.
    The main result of this paper is Theorem 3.1 which is a criterion for weak o-minimality of a linearly ordered structure in terms of realizations of 1-types. Here we also prove some other properties of weakly o-minimal structures. In particular, we characterize all weakly o-minimal linear orderings in the signature $\{ . Moreover, we present a criterion for density of isolated types of a weakly o-minimal theory. Lastly, at the end of the paper we present some remarks on the Exchange (...)
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  • On ℵ0-categorical weakly o-minimal structures.B. Herwig, H. D. Macpherson, G. Martin, A. Nurtazin & J. K. Truss - 1999 - Annals of Pure and Applied Logic 101 (1):65-93.
    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 (...)
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  • A version of o-minimality for the p-adics.Deirdre Haskell & Dugald Macpherson - 1997 - Journal of Symbolic Logic 62 (4):1075-1092.
  • Elimination of quantifiers for ordered valuation rings.M. A. Dickmann - 1987 - Journal of Symbolic Logic 52 (1):116-128.
  • Lattice Ordered O -Minimal Structures.Carlo Toffalori - 1998 - Notre Dame Journal of Formal Logic 39 (4):447-463.
    We propose a notion of -minimality for partially ordered structures. Then we study -minimal partially ordered structures such that is a Boolean algebra. We prove that they admit prime models over arbitrary subsets and we characterize -categoricity in their setting. Finally, we classify -minimal Boolean algebras as well as -minimal measure spaces.
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  • Expansion of a model of a weakly o-minimal theory by a family of unary predicates.Bektur Sembiuly Baizhanov - 2001 - Journal of Symbolic Logic 66 (3):1382-1414.
    A subset A $\subseteq$ M of a totally ordered structure M is said to be convex, if for any a, b $\in A: [a . A complete theory of first order is weakly o-minimal (M. Dickmann [D]) if any model M is totally ordered by some $\emptyset$ -definable formula and any subset of M which is definable with parameters from M is a finite union of convex sets. We prove here that for any model M of a weakly o-minimal theory (...)
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  • Small theories of Boolean ordered o-minimal structures.Roman Wencel - 2002 - Journal of Symbolic Logic 67 (4):1385-1390.
    We investigate small theories of Boolean ordered o-minimal structures. We prove that such theories are $\aleph_{0}-categorical$ . We give a complete characterization of their models up to bi-interpretability of the language. We investigate types over finite sets, formulas and the notions of definable and algebraic closure.
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