SETS DEFINABLE IN ORDERED ABELIAN GROUPS OF FINITE BURDEN (Model theoretic aspects of the notion of independence and dimension)

1. Hans Adler, Strong theories, burden, and weight, available at http://www.logic.univie.ac.at/~adler/docs/strong.pdf,

2007.

2. Alfred Dolich and John Goodrick, Strong theories of ordered abelian groups, Fundamenta Mathematicae 23 (2017),

269-296.

3. _ _ _ , Tame topology over definable uniform structures, Notre Dame Journal of Formal Logic to appear (2022).

4. _ _ _ , Discrete sets definable in strong expansions of ordered Abelian groups, arXiv:2208.06929, 2023.

5. _ _ _ , Topological properties of definable sets in ordered Abelian groups of burden 2, Mathematical Logic Quarterly

(2023).

6. John Goodrick, A monotonicity theorem for dp-minimal densely ordered groups, Journal of Symbolic Logic 75 (2010),

no. 1, 221-238.

7. _ _ _ , Definable sets in dp-minimal ordered Abelian groups, RIMS Ki\kyuroku (Model theoretic aspects of the notion

of independence and dimension) (2022), no. 2218.

8. Yuri Gurevich and P. H. Schmitt, The theory of ordered abelian groups does not have the independence property,

Transactions of the American Mathematical Society 284 (1984), no. 1, 171-182.

9. Chris Miller, Expansions of dense linear orders with the intermediate value property, The Journal of Symbolic Logic

66 (2001), 1783-1790.

10. Saharan Shelah, Strongly dependent theories, Israel Journal of Mathematics 204 (2014), no. 1, 1-83,

arXiv:math/0504197v3.

11. Pierre Simon, On dp-minimal ordered structures, The Journal of Symbolic Logic 76 (2011), no. 2, 448-460.

12. - - - , A guide to NIP theories, Cambridge University Press, 2015.

DEPARTMENT OF MATHEMATICS, UNIVERSIDAD DE LOS ANDES, CARRERA 1 # 18A-12, BOGOTA, COLOMBIA

Email address: j r. goodrick427©uniandes. edu. co

...