### Heike Mildenberger

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### Publications and Preprints

• On the homogeneity property for certain quantifier logics, Archive for Mathematical Logic 31:445-455 (1992).
• A rigid Boolean algebra that admits the elimination of Q^2_1 , Fundamenta Mathematicae 142:1-18 (1993).
• Ordertypes of Free Subsets, Annals of Pure and Applied Logic 89:75-83 (1997).
• Non-Constructive Galois-Tukey Connections, The Journal of Symbolic Logic 62:1179-1187 (1997).
• Changing cardinal invariants of the reals without changing cardinals or the reals, The Journal of Symbolic Logic 63:593-599 (1998).
• Borel on the question versus Borel on the answers, Mathematical Logic Quarterly 45:127-133 (1999).
• Together with Otmar Spinas: Meeting infinitely many cells of a partition once, Archive for Mathematical Logic 37:495-503 (1998).
• Together with Andreas Blass: On the cofinality of ultrapowers, Journal of Symbolic Logic 64:627-636 (1999).
• Groupwise dense families, Archive for Mathematical Logic 40:93-112 (2001).
• Toeplitz Matrices and Convergence, Fundamenta Mathematicae 165 (2000), 175-189.
• Joint work with Sakae Fuchino, Saharon Shelah and Peter Vojtas: On absolutely divergent series[MShFV:593], Fundamenta Mathematicae 62:252-268 (1999).
• 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).
• The strengths of some violations of covering, Mathematical Logic Quarterly 47:291-298 (2001).
• Joint work with Saharon Shelah, [MdSh:731], The relative consistency of g < cf(Sym(omega)), Journal of Symbolic Logic 67:297-314 (2002).
• Joint work with Saharon Shelah, [MdSh:753], The splitting number can be smaller than the matrix chaos number, Fundamenta Mathematicae 171:167-176 (2002).
• No Borel connections for the unsplitting relations, Mathematical Logic Quarterly 48:517-521 (2002).
• Joint work with Saharon Shelah, [MdSh:778], Specializing Aronszajn trees by countable approximations, Archive for Mathematical Logic 42:627-647 (2003).
• Joint work with Saharon Shelah, [MdSh:725], On needed reals, Israel Journal of Mathematics, 141:1-38 (2004).
• More canonical forms and dense free subsets, Annals of Pure and Applied Logic 125:75-99 (2004).
• 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).
• Creatures on \omega_1 and Weak Diamonds, The Journal of Symbolic Logic 74:1-16 (2009).
• 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).
• Joint work with Saharon Shelah and Boaz Tsaban, The combinatorics of \tau-covers [MdShTs:858], Topology and its Applications 154(1):263-276 (2007).
• On the groupwise density number for filters, Acta Univ. Carolinae - Math. et Phys. 46(2):55-63 (2005).
• 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.
• There may be infinitely many near coherence classes under ${\mathfrak u}<{\mathfrak d}$, The Journal of Symbolic Logic 72(4):1228-1238 (2007).
• 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).
• 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.
• 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).
• Cardinal characteristics for Menger-bounded subgroups, Topology and its Applications 156:130-137 (2008).
• Finding generic filters by playing games, Archive for Mathematical Logic 49(1):91-118 (2010).
• The club principle and the distributivity number, The Journal of Symbolic Logic 76(1):34-46 (2011).
• Joint work with Lyubomyr Zdomskyy, $L$-spaces and the $P$-ideal dichotomy, Acta Math. Hung. 125 (1-2):87-97 (2009).
• Joint work with Saharon Shelah, Proper Translation, Fundamenta Mathematicae 125 no. 1 (2011), 1-38.
• On Milliken-Taylor ultrafilters, Notre Dame Journal of Formal Logic 52 no. 4 (2011), 381-394.
• 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.
• Joint with Saharon Shelah, Many countable support iterations of proper forcings preserve Souslin trees, Annals of Pure and Appl. Logic 165, 2014, 573-608.
• Joint with Dilip Raghavan and Juris Streprans, Splitting families and complete separability, Canad. Math. Bull. 57 (2014), no. 1, 119-124.
• together with Taras Banakh, Cardinal invariants distinguishing permutation groups, European Journal of Mathematics, 2:2 (2016) 493-507.
• Diagonalising an Ultrafilter and Preserving a $P$-Point, Fund. Math. 246 (2019), no. 1, 9-26.
• Joint with Saharon Shelah, Specialising Aronszajn Trees with Strong Axiom A and with Halving, Notre Dame J. Form. Log. 60 (2019), no. 4, 587-616.
• joint with Filippo Calderoni and Luca Motto Ros, Uncountable structures are not classifiable up to bi-embeddability, J. Math. Log. 20 (2020), no. 1, 2050001, 49 pp.
• joint with S. Shelah, A version of $\kappa$-Miller forcing, Archive for Mathematical Logic, 59(7) (2020), 879 - 892
• Joint with Saharon Shelah, The cofinality of the symmetric group and the cofinality of ultrapowers, Israel J. Math. 242 (2021), no. 1, 97 - 128.
• Joint with Saharon Shelah, Higher Miller Forcing May Collapse Cardinals, J. Symb. Log. 86 (2021), no. 4, 1721 - 1744.

• Joint with Maxwell Levine, Distributivity of uncountably singular tree forcings, to appear in the Israel Journal of Mathematics.
• Joint with Giorgio Laguzzi and Brendan Stuber-Rousselle, Mathias and Silver Forcing Parametrized by Density, to appear in Archive Math. Logic.
• Joint with Christian Bräuninger, A Simple $P_{\aleph_1}$-Point and a Simple $P_{\aleph_2}$-Point, to appear in the Journal of the European Mathematical Society.
• Joint with Giorgio Laguzzi and Brendan Stuber-Rousselle, On splitting trees, to appear in Mathematical Logic Quarterly.
• Exactly Two and Exactly Three Near-Coherence Classes, 2022, to appear in the Journal of Mathematical Logic.
• joint with Shelah, Negating Club and Stick with Strategically Closed Forcings 2022, preprint.
• Last update February 3, 2023, HM