# Heike Mildenberger

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### Publications and theses

1. Entscheidbare und unentscheidbare Theorien von linearen Ordnungen, Diplomarbeit, 180 pp., Freiburg im Breisgau 1987.
2. Homogenitätseigenschaften in Erweiterungslogiken, Dissertation, 150 pp., Freiburg im Breisgau 1990.
3. On the homogeneity property for certain quantifier logics, Archive for Mathematical Logic 31:445-455 (1992).
4. A rigid Boolean algebra that admits the elimination of Q^2_1 , Fundamenta Mathematicae 142:1-18 (1993).
5. Ordertypes of Free Subsets, Annals of Pure and Applied Logic 89:75-83 (1997).
6. Non-Constructive Galois-Tukey Connections, The Journal of Symbolic Logic 62:1179-1187 (1997).
7. Changing cardinal invariants of the reals without changing cardinals or the reals, The Journal of Symbolic Logic 63:593-599 (1998).
8. Contributions to the Theory of Cardinal Characteristics, Habilitationsschrift, 125 pp, Universität Bonn 1998.
9. Borel on the question versus Borel on the answers, Mathematical Logic Quarterly 45:127-133 (1999).
10. Together with Otmar Spinas: Meeting infinitely many cells of a partition once, Archive for Mathematical Logic 37:495-503 (1998).
11. Together with Andreas Blass: On the cofinality of ultrapowers, Journal of Symbolic Logic 64:627-636 (1999).
12. Groupwise dense families, Archive for Mathematical Logic 40:93-112 (2001).
13. Toeplitz Matrices and Convergence, Fundamenta Mathematicae 165 (2000), 175-189.
14. Joint work with Sakae Fuchino, Saharon Shelah and Peter Vojtas: On absolutely divergent series[MShFV:593], Fundamenta Mathematicae 62:252-268 (1999).
15. Joint work with Saharon Shelah: Changing cardinal characteristics without adding omega-sequences or changing cofinalities [MdSh:684], Annals of Pure and Applied Logic 106:207-261 (2000).
16. The strengths of some violations of covering, Mathematical Logic Quarterly 47:291-298 (2001).
17. Joint work with Saharon Shelah, [MdSh:731], The relative consistency of g < cf(Sym(omega)), Journal of Symbolic Logic 67:297-314 (2002).
18. Joint work with Saharon Shelah, [MdSh:753], The splitting number can be smaller than the matrix chaos number, Fundamenta Mathematicae 171:167-176 (2002).
19. No Borel connections for the unsplitting relations, Mathematical Logic Quarterly 48:517--521 (2002).
20. Joint work with Saharon Shelah, [MdSh:778], Specializing Aronszajn trees by countable approximations, Archive for Mathematical Logic 42:627--647 (2003).
21. Joint work with Saharon Shelah, [MdSh:725], On needed reals, Israel Journal of Mathematics, 141:1-38 (2004).
22. More canonical forms and dense free subsets, Annals of Pure and Applied Logic 125:75-99 (2004).
23. Joint work with Saharon Shelah and Boaz Tsaban, Covering the Baire space by families which are not finitely dominating, [MShT:847], Annals of Pure and Applied Logic 140:60-71 (2006). (In the background of the photo, on the blackboard, you can read about Cantor's dream.)
24. Creatures on \omega_1 and Weak Diamonds, The Journal of Symbolic Logic 74:1-16 (2009).
25. Joint work with Saharon Shelah, Increasing the groupwise density number by c.c.c. forcing, [MdSh:843], Annals of Pure and Applied Logic, 149:6-13 (2007).
26. Joint work with Saharon Shelah and Boaz Tsaban, The combinatorics of \tau-covers [MdShTs:858], Topology and its Applications 154(1):263-276 (2007).
27. On the groupwise density number for filters, Acta Univ. Carolinae - Math. et Phys. 46(2):55-63 (2005).
28. Forcing with $F_\sigma$- and with Summable Filters, Quaderni di Matematica, vol. 17 (2006), Set Theory: Recent Trends and Applications, ed. by A. Andretta, pages 183-194.
29. There may be infinitely many near coherence classes under ${\mathfrak u}<{\mathfrak d}$, The Journal of Symbolic Logic 72(4):1228-1238 (2007).
30. Joint work with Saharon Shelah, Specialising Aronszajn trees and preserving some weak diamonds, [MdSh:848], The Journal of Applied Analysis 15(1):47-78 (2009).
31. The filter generated by {A+A : A subseteq N} is comeagre and pinning down some cardinals, Quaderni di Matematica vol. 18 (2007), Selection principles and games in Topology, ed. L. Kocinac, pages 101-103.
32. Joint work Saharon Shelah, The principle of near coherence of filters does not imply the filter dichotomy principle, [MdSh:894], The Transactions of the American Mathematical Society 361:2305-2317 (2009).
33. Cardinal characteristics for Menger-bounded subgroups, Topology and its Applications 156:130-137 (2008).
34. Finding generic filters by playing games, Archive for Mathematical Logic 49(1):91-118 (2010).
35. The club principle and the distributivity number, The Journal of Symbolic Logic 76(1):34-46 (2011).
36. Joint work with Lyubomyr Zdomskyy, $L$-spaces and the $P$-ideal dichotomy, Acta Math. Hung. 125 (1-2):87-97 (2009).
37. Joint work with Saharon Shelah, Proper Translation, Fundamenta Mathematicae 125 no. 1 (2011), 1-38.
38. On Milliken-Taylor ultrafilters, Notre Dame Journal of Formal Logic 52 no. 4 (2011), 381-394.
39. Joint with Saharon Shelah The minimal cofinality of an ultrapower of omega and the cofinality of the symmetric group can be larger than b+, The Journal of Symbolic Logic 76, no. 4 (2011), 1322-1340.
40. Joint with Saharon Shelah, Many countable support iterations of proper forcings preserve Souslin trees, Annals of Pure and Appl. Logic 165, 2014, 573-608.
41. Joint with Dilip Raghavan and Juris Streprans, Splitting families and complete separability, Canad. Math. Bull. 57 (2014), no. 1, 119-124.
42. together with Taras Banakh, Cardinal invariants distinguishing permutation groups, European Journal of Mathematics, 2:2 (2016) 493-507.
43. Joint with Saharon Shelah, The cofinality of the symmetric group and the cofinality of ultrapowers, preprint, October 2016
44. Joint with Saharon Shelah, Specialising Aronszajn Trees with Strong Axiom A and with Halving preprint, November 2016
45. Diagonalising an Ultrafilter and Preserving a $P$-Point preprint, May 2016