Forking geometry on theories with an independent predicate

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• 作者：Juan Felipe Carmona (1) (2)
  
  1. Universidad de Los Andes ; Cra 1 No 18A-10 ; Bogot谩 ; Colombia
  2. Institut Camille Jordan UMR5208 ; Universit茅 Lyon 1 ; Universit茅 de Lyon CNRS ; 43 boulevard du 11 novembre 1918 ; 69622 ; Villeurbanne Cedex ; France
  
• 关键词：Geometric structures ; U ; rank one theories ; n ; Ample theories ; Strongly dependent theories ; Definable groups ; 03C45
• 刊名：Archive for Mathematical Logic
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：54
• 期：1-2
• 页码：247-255
• 全文大小：148 KB
• 参考文献：1. Baudisch A., Pillay A.: A free pseudospace. J. Symb. Log. 65, 443鈥?60 (2000) CrossRef
  2. Baudisch, A., Martin-Pizarro, A., Ziegler, M.: Ample hierarchy. Fund. Math. 224, 97鈥?53 (2014)
  3. Berenstein, A., Vassiliev, E.: Geometric structures with an independent subset. MODNET (Preprint)
  4. Berenstein A., Vassiliev E.: On lovely pairs of geometric structures. Ann. Pure Appl. Log. 161(7), 866鈥?78 (2010) CrossRef
  5. Evans D.: Ample dividing. J. Symb. Log. 68, 1385鈥?402 (2003) CrossRef
  6. Hrushovski E., Pillay A.: Weakly normal groups. Log. Colloq. 85, 233鈥?44 (1987)
  7. Pillay A.: The geometry of forking and groups of finite Morley rank. J. Symb. Log. 60(4), 1251鈥?259 (1995) CrossRef
  8. Pillay A.: A note on CM-triviality and the geometry of forking. J. Symb. Log. 65(1), 474鈥?80 (2000) CrossRef
  9. Tent, K.: The free pseudospace is / n-ample, but not ( / n +聽 1)-ample. J. Symb. Log. 79(2), 410鈥?28 (2014)
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematical Logic and Foundations
  Mathematics
  Algebra
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0665

文摘

We prove that a simple theory of SU-rank 1 is n-ample if and only if the associated theory equipped with a predicate for an independent dense subset is n-ample for n at least 2.