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O-stable ordered groups

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Abstract

An ordered structure M is said to be o-λ-stable if, for every A ⊆ M with |A| ≤ λ and every cut in M, at most λ 1-types over A are consistent with the cut. In the present article, we prove that every o-stable group is abelian. We also study definable subsets and unary functions of o-stable groups.

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Authors and Affiliations

  1. Suleyman Demirel University, Kaskelen, 040900, Kazakhstan

    V. V. Verbovskiĭ

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  1. V. V. Verbovskiĭ
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Correspondence to V. V. Verbovskiĭ.

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Original Russian Text © V. V. Verbovskiĭ, 2010, published in Matematicheskie Trudy, 2010, Vol. 13, No. 2, pp. 84–127.

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Verbovskiĭ, V.V. O-stable ordered groups. Sib. Adv. Math. 22, 50–74 (2012). https://doi.org/10.3103/S105513441201004X

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  • DOI: https://doi.org/10.3103/S105513441201004X

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