Minimality conditions on circularly ordered structures

Mathematical Logic Quarterly 51 (4):377-399 (2005)
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We explore analogues of o-minimality and weak o-minimality for circularly ordered sets. Much of the theory goes through almost unchanged, since over a parameter the circular order yields a definable linear order. Working over ∅ there are differences. Our main result is a structure theory for ℵ0-categorical weakly circularly minimal structures. There is a 5-homogeneous example which is not 6-homogeneous, but any example which is k-homogeneous for some k ≥ 6 is k-homogeneous for all k



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Citations of this work

On ℵ0‐categorical weakly circularly minimal structures.Beibut Sh Kulpeshov - 2006 - Mathematical Logic Quarterly 52 (6):555-574.
On weakly circularly minimal groups.Beibut Sh Kulpeshov & Viktor V. Verbovskiy - 2015 - Mathematical Logic Quarterly 61 (1-2):82-90.

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References found in this work

On variants of o-minimality.Dugald Macpherson & Charles Steinhorn - 1996 - Annals of Pure and Applied Logic 79 (2):165-209.
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.
Weakly o-minimal structures and some of their properties.B. Sh Kulpeshov - 1998 - Journal of Symbolic Logic 63 (4):1511-1528.

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