Heike Mildenberger
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).
Corrected version:
The club principle and a large continuum.
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, Israel J. Math. 261 (2024), no. 2, 549--588.
Joint with Giorgio Laguzzi and Brendan Stuber-Rousselle,
Mathias and Silver Forcing Parametrized by Density,
Arch. Math. Logic 62 (2023), no. 7-8, 96--990,
printed version, via open access.
Joint with Christian Bräuninger,
A Simple $P_{\aleph_1}$-Point and a Simple $P_{\aleph_2}$-Point, J. Eur. Math. Soc. 25 (2023), no. 12, 4971--4996.
DOI 10.4171/JEMS/1299.
Joint with Giorgio Laguzzi and Brendan Stuber-Rousselle,
On splitting trees,
Mathematical Logic Quarterly 2023;69:1--30. printed version, via open access.
Exactly Two
and Exactly Three Near-Coherence Classes,
Journal of Mathematical Logic.
Volume No. 24, Issue No. 01, Article No. 2350003, Year 2024.
DOI 10.1142/S0219061323500034
joint with Saharon Shelah, Forcing Diamond and Applications to Iterability, April 2025, preprint, revised version September 2026. To appear in the Israel Journal of Mathematics.
joint with Saharon Shelah,
Negating Club and Stick with Strategically Closed Forcings
October 2022, preprint.
joint with Maxwell Levine,
Good Scales and Non-Compactness of Squares 2025,
revised in July 2026, preprint.
Last update Sept. 2029, HM
