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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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[1]Adler, Hans, Strong theories, burden, and weight, preprint, 2007.
[2]Chernikov, Artem, Theories without tree property of the second kind, in preparation.
[3]Chernikov, Artem and Kaplan, Itay, Forking and dividing in NTP2 theories, submitted, Available asarXiv:0906.2806vl [math.LO].
[4]Dolich, Alfred, Goodrick, John, and Lippel, David, Dp-minimality: basic facts and examples, Modnet preprint 207.
[5]Goodrick, John, A monotonicity theorem for dp-minimal densely ordered groups, this Journal, vol. 75 (2010), no. 1, pp. 221238.
[6]Macpherson, Dugald and Steinhorn, Charles, On variants o-minimality, Annals of Pure and Applied Logic, vol. 79 (1996), pp. 165209.
[7]Onshuus, Alf and Usvyatsov, Alex, On dp-minimality, strong dependence, and weight, submitted.
[8]Parigot, Michel, Théories d'arbres, this Journal, vol. 47 (1982), pp. 841853.
[9]Poizat, Bruno, Cours de théorle des modèles, Nur al-Mantiq wal-Mari'fah.
[10]Rubin, Matatyahu, Theories of linear order, Israel Journal of Mathematics, vol. 17 (1974), no. 4, pp. 392443.
[11]Schmerl, James H., Partially ordered sets and the independence property, this Journal, vol. 54 (1989), no. 2.
[12]Shelah, Saharon, Classification theory for elementary classes with the dependence property - a modest beginning, Scientlae Mathematlcae Japontcae, vol. 59 (2004), no. 2, pp. 263316.
[13]Shelah, Saharon, Dependent first order theories, continued, Israel Journal of Mathematics, vol. 173 (2009).
[14]Shelah, Saharon, Strongly dependent theories, 863.
[15]Shelah, Saharon, Dependent theories and the generic pair conjecture, 900.
[16]Simonetta, Patrick, 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]Wagner, Frank O., 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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