Skip to main content



We show that dp-minimal valued fields are henselian and give classifications of dp-minimal ordered abelian groups and dp-minimal ordered fields without additional structure.

Hide All
[1] Aschenbrenner M., Dolich A., Haskell D., Macpherson D., and Starchenko S., Vapnik-Chervonenkis density in some theories without the independence property , Transaction of the American Mathematical Society, (2016), 58895949.
[2] Aschenbrenner M., Dolich A., Haskell D., Macpherson D., and Starchenko S., Vapnik-Chervonenkis density in some theories without the independence property , Notre Dame Journal of Formal Logic, vol. 54 (2013), no. 3, 4, pp. 311363.
[3] Chernikov A. and Simon P., Henselian valued fields and inp-minimality, preprint, 2015.
[4] Cluckers R. and Halupczok I., Quantifier elimination in ordered abelian groups . Confluentes Mathematici, vol. 3 (2011), no. 4, pp. 587615.
[5] Engler A. J. and Prestel A., Valued Fields, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2005.
[6] Goodrick J., A monotonicity theorem for dp-minimal densely ordered groups, this Journal, vol. 75 (2010), no. 1, pp. 221238.
[7] Guingona V., On vc-minimal fields and dp-smallness . Archive for Mathematical Logic, vol. 53 (2014), no. 5, 6, pp. 503517.
[8] Jahnke F. and Koenigsmann J., Uniformly defining p-henselian valuations . Annals of Pure and Applied Logic, vol. 166 (2015), no. 7, 8, pp. 741754.
[9] Johnson W., On dp-minimal fields, preprint, 2015.
[10] Kaplan I., Scanlon T., and Wagner F. O., Artin-Schreier extensions in NIP and simple fields . Israel Journal of Mathematics, vol. 185 (2011), pp. 141153.
[11] Kudaĭbergenov K. Zh., Weakly quasi-o-minimal models . Turkish Journal of Mathematics, vol. 13 (2010), no. 1, pp. 156168.
[12] Macintyre A., McKenna K., and van den Dries L., Elimination of quantifiers in algebraic structures . Advances in Mathematics, vol. 47 (1983), no. 1, pp. 7487.
[13] Macpherson D., Marker D., and Steinhorn C., Weakly o-minimal structures and real closed fields . Transactions of the American Mathematical Society, vol. 352 (2000), pp. 54355483.
[14] Onshuus A. and Usvyatsov A., On dp-minimality, strong dependence and weight, this Journal, vol. 76 (2011), no. 3, pp. 737758.
[15] Prestel A. and Delzell C. N., Mathematical Logic and Model Theory, Universitext, Springer, 2011.
[16] Prestel A. and Ziegler M., Model-theoretic methods in the theory of topological fields . Journal für die Reine und Angewandte Mathematik, vol. 299 (1978), no. 300, pp. 318341.
[17] Simon P., On dp-minimal ordered structures, this Journal, vol. 76 (2011), pp. 448460.
[18] Simon P., Dp-minimality: Invariant types and dp-rank, this Journal, vol. 79 (2014), pp. 10251045.
[19] Simon P., A Guide to NIP Theories, Lecture Notes in Logic. Cambridge University Press, Cambridge, 2015.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 36 *
Loading metrics...

Abstract views

Total abstract views: 68 *
Loading metrics...

* Views captured on Cambridge Core between 21st March 2017 - 12th December 2017. This data will be updated every 24 hours.