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On uniform definability of types over finite sets

  • Vincent Guingona (a1)


In this paper, using definability of types over indiscernible sequences as a template, we study a property of formulas and theories called “uniform definability of types over finite sets” (UDTFS). We explore UDTFS and show how it relates to well-known properties in model theory. We recall that stable theories and weakly o-minimal theories have UDTFS and UDTFS implies dependence. We then show that all dp-minimal theories have UDTFS.


Corresponding author

Department of Mathematics, University of Notre Dame, 255 Hurley, Notre Dame, IN 46556, USA


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[2] Dolich, A., Goodrick, J., and Lippel, D., dp-Minimality: Basic facts and examples, preprint, 07 2009.
[3] Goodrick, J., A monotonicity theorem for dp-minimal densely ordered groups, this Journal, vol. 75 (2010), no. 1, pp. 221238.
[4] Johnson, H. R. and Laskowski, M. C., Compression schemes, stable definable families, and o-minimal structures, Discrete & Computational Geometry, vol. 43 (2010), pp. 914926.
[5] Onshuus, A. and Usvyatsov, A., On dp-minimality, strong dependence, and weight, this Journal, vol. 76 (2011), no. 3, pp. 737758.
[6] Shelah, S., Classification theory and the number of non-isomorpkic models, North-Holland Publishing Company, 1978.
[7] Simon, P., On dp-minimal ordered structures, preprint, 09 2009.
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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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