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On dp-minimal ordered structures

  • Pierre Simon (a1)

We show basic facts about dp-minimal ordered structures. The main results are: dp-minimal groups are abelian-by-finite-exponent, in a divisible ordered dp-minimal group, any infinite set has nonempty interior, and any theory of pure tree is dp-minimal.

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[6] Dugald Macpherson and Charles Steinhorn , On variants o-minimality, Annals of Pure and Applied Logic, vol. 79 (1996), pp. 165209.

[10] Matatyahu Rubin , Theories of linear order, Israel Journal of Mathematics, vol. 17 (1974), no. 4, pp. 392443.

[13] Saharon Shelah , Dependent first order theories, continued, Israel Journal of Mathematics, vol. 173 (2009).

[16] Patrick Simonetta , An example of a c-minimal group which is not abelian-by-finite, Proceedings of the American Mathematical Society, vol. 131 (2003), no. 12, pp. 39133917.

[17] Frank O. Wagner , Simple theories, Mathematics and Its Applications, 503, Kluwer Academic Publishers, 2000.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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