Publications of L. Halbeisen

Publications of Lorenz Halbeisen

Diploma, Thesis, and Habilitation

Books

  1. Combinatorial Set Theory: with a gentle introduction to forcing (pdf)
    Springer-Verlag, London (2012) [book details]

  2. Mit harmonischen Verhältnissen zu Kegelschnitten, Perlen der klassischen Geometrie (ausgewählte Kapitel) (with Norbert Hungerbühler and Juan Läuchli)
    Springer-Verlag, Heidelberg (2016) [book details]

  3. Combinatorial Set Theory: with a gentle introduction to forcing (revised and extended second edition)
    Springer-Verlag, London (2017) [book details] [errata]

  4. Gödel's Theorems and Zermelo's Axioms: a firm foundation of mathematics (with Regula Krapf)
    Birkhäuser-Verlag, Basel (2020) [book details] [errata]

  5. Mit harmonischen Verhältnissen zu Kegelschnitten, Perlen der klassischen Geometrie (erweiterte zweite Auflage) (with Norbert Hungerbühler and Juan Läuchli)
    Springer-Verlag, Heidelberg (2021) [book details]

  6. Eine Entdeckungsreise in die Welt des Unendlichen, die Grundlagen der Mathematik von der Antike bis in die Neuzeit (with Regula Krapf)
    Springer Spektrum, Berlin (2023) [book details]

Research

    Infinite Combinatorics

    Combinatorial Set Theory, Generalized Ramsey Theory, Set Theory without the Axiom of Choice, Combinatorics of Forcing Constructions, Combinatorial Methods in Banach Space Theory, Set-Theoretic Topology, Combinatorial Aspects of Algebra

  1. Consequences of arithmetic for set theory (pdf) [abstract] (with Saharon Shelah),
    The Journal of Symbolic Logic, 59 (1994) 30-40

  2. Mathias absoluteness and the Ramsey property (pdf) [abstract] (with Haim Judah),
    The Journal of Symbolic Logic, 61 (1996) 177-193

  3. On shattering, splitting and reaping partitions (pdf) [abstract],
    Mathematical Logic Quarterly, 44 (1998) 123-134

  4. Symmetries between two Ramsey properties (pdf) [abstract],
    Archive for Mathematical Logic, 37(4) (1998) 241-260

  5. The cardinality of Hamel bases of Banach spaces (pdf) [abstract] (with Norbert Hungerbühler),
    East-West Journal of Mathematics, 2(2) (2000) 153-159

  6. Techniques for approaching the dual Ramsey property in the projective hierarchy (pdf) [abstract] (with Benedikt Löwe),
    Pacific Journal of Mathematics, 200(1) (2001) 119-145

  7. Ramseyan ultrafilters (pdf) [abstract],
    Fundamenta Mathematicae, 169(3) (2001) 233-248

  8. Ultrafilter spaces on the semilattice of partitions (pdf) [abstract] (with Benedikt Löwe),
    Topology and its Applications, 115(3) (2001) 317-332

  9. On the complexity of Hamel bases of infinite dimensional Banach spaces (pdf) [abstract],
    Colloquium Mathematicum, 89 (2001) 133-134

  10. Relations between some cardinals in the absence of the axiom of choice (pdf) [abstract] (with Saharon Shelah),
    The Bulletin of Symbolic Logic, 7(2) (2001) 237-261

  11. On continuously Urysohn and strongly separating spaces (pdf) [abstract] (with Norbert Hungerbühler),
    Topology and its Applications, 118(3) (2002) 329-335

  12. A result in dual Ramsey theory (pdf) [abstract] (with Pierre Matet),
    Journal of Combinatorial Theory (A), 100 (2002) 394-398

  13. Making doughnuts of Cohen reals (pdf) [abstract],
    Mathematical Logic Quarterly, 49(2) (2003) 173-178

  14. A generalization of the dual Ellentuck theorem (pdf) [abstract] (with Pierre Matet),
    Archive for Mathematical Logic, 42(2) (2003) 103-128

  15. On the cardinality of smallest spanning sets of rings (pdf) [abstract] (with Nadia Boudi),
    Quaestiones Mathematicae, 26(3) (2003) 321-325

  16. On a theorem of Banach and Kuratowski and K-Lusin sets (pdf) [abstract] (with Tomek Bartoszynski),
    Rocky Mountain Journal of Mathematics, 33(4) (2003) 1223-1231

  17. A set-theoretic approach to complete minimal systems in Banach spaces of bounded functions (pdf) [abstract],
    Matematychni Studii, 20(2) (2003) 162-166

  18. On asymptotic models in Banach spaces (pdf) [abstract] (with Edward Odell),
    Israel Journal of Mathematics, 139 (2004) 253-291

  19. Silver measurability and its relation to other regularity properties (pdf) [abstract] (with Jörg Brendle and Benedikt Löwe),
    Mathematical Proceedings of the Cambridge Philosophical Society, 138(1) (2005) 135-149

  20. A number-theoretic conjecture and its implication for set theory (pdf) [abstract],
    Acta Mathematica Universitatis Comenianae, 74(2) (2005) 243-254

  21. On bases in Banach spaces (pdf) [abstract] (with Tomek Bartoszynski, Mirna Dzamonja, Eva Murtinova, Anatolij Plichko, all-5-pic),
    Studia Mathematica, 170(2) (2005) 147-171

  22. Families of almost disjoint Hamel bases (pdf) [abstract],
    Extracta Mathematicae, 20(2) (2005) 199-202

  23. A playful approach to Silver and Mathias forcings (pdf) [abstract],
    Foundations of the Formal Sciences V: Infinite Games (Papers of a Conference held in Bonn, November 26-29, 2004)
    College Publications: Studies in Logic (vol. 11), London (2007), 123-142

  24. Non-separable Banach spaces with non-meager Hamel basis (pdf) [abstract] (with Taras Banakh and Mirna Dzamonja),
    Studia Mathematica, 189(1) (2008) 27-34

  25. Comparing cardinalities in Zermelo's system (pdf) [abstract],
    Cahiers du Centre de Logique, 17 (2010) 9-19

  26. Über ein Theorem von Hans Läuchli (pdf) [abstract],
    Elemente der Mathematik, 72(4) (2017) 164-170

  27. On Ramsey choice and partial choice for infinite families of n-element sets (pdf) [abstract] (with Eleftherios Tachtsis),
    Archive for Mathematical Logic, 59(5) (2020) 583-606

  28. A weird relation between two cardinals (pdf) [abstract],
    Archive for Mathematical Logic, 57 (2018) 593-599

  29. Magic sets (pdf) [abstract] (with Marc Lischka and Salome Schumacher),
    Real Analysis Exchange, 43 (2018) 187-204

  30. Forms of choice in ring theory (pdf) (with Norbert Hungerbühler, Nir Lazarovich, Waltraud Lederle, Marc Lischka, Salome Schumacher),
    Results in Mathematics, 74 (2019) no.1 Article:14

  31. Halfway new cardinal characteristics (pdf) (with Jörg Brendle, Lukas Daniel Klausner, Marc Lischka, and Saharon Shelah),
    Annals of Pure and Applied Logic (to appear)

  32. A new weak choice principle (pdf) (with Riccardo Plati and Salome Schumacher),
    The Journal of Symbolic Logic (to appear)

  33. On Carruth's axioms for natural sums and products (pdf) (with Pedro Pablo Pérez Velasco),
    European Journal of Mathematics, 9(4) (2023) Article:97

  34. Four cardinals and their relations in ZF (pdf) (with Riccardo Plati, Salome Schumacher, and Saharon Shelah),
    Annals of Pure and Applied Logic, 174(2) (2023) (doi)

  35. Some implications of Ramsey Choice for families of n-element sets (pdf)(with Salome Schumacher),
    Archive for Mathematical Logic, 62(5-6) (2023) 703-733 (doi)

  36. Implications of Ramsey Choice Principles in ZF (pdf) (with Riccardo Plati and Saharon Shelah), 9 pages, submitted


    37. Finite Combinatorics and Geometry

    Number Theory, Extremal Combinatorics, Graph Theory, Ramsey Theory, Enumerative Combinatorics, Design Theory, Combinatorics on Words, Dynamical Systems, Geometry, Elliptic Curves

  37. The general counterfeit coin problem (pdf) [abstract] (with Norbert Hungerbühler),
    Discrete Mathematics, 147 (1995) 139-150

  38. The Josephus problem (pdf) [abstract] (with Norbert Hungerbühler),
    Journal de Théorie des Nombres de Bordeaux, 9 (1997) 303-318

  39. Optimal bounds for the length of rational Collatz cycles (pdf) [abstract] (with Norbert Hungerbühler),
    Acta Arithmetica, LXXVIII (1997) 227-239

  40. Packings in complete graphs (pdf) [abstract] (with Norbert Hungerbühler),
    Ars Combinatoria, 48 (1998) 97-110

  41. Powers and polynomials in Zm (pdf) [abstract] (with Norbert Hungerbühler and Hans Läuchli),
    Elemente der Mathematik, 54(3) (1999) 118-129

  42. Über das Mischen von Spielkarten, ein mathematisches Menü (pdf) [abstract] (with Stephanie Gloor),
    Elemente der Mathematik, 54(4) (1999) 156-162

  43. On generalized Carmichael numbers (pdf) [abstract] (with Norbert Hungerbühler),
    Hardy-Ramanujan Journal, 22 (1999) 8-22

  44. Number theoretic aspects of a combinatorial function (pdf) [abstract] (with Norbert Hungerbühler),
    Notes on Number Theory and Discrete Mathematics, 5 (1999) 138-150

  45. Generation of isospectral graphs (pdf) [abstract] (with Norbert Hungerbühler),
    Journal of Graph Theory, 31 (1999) 255-265

  46. Reconstruction of weighted graphs by their spectrum (pdf) [abstract] (with Norbert Hungerbühler),
    European Journal of Combinatorics, 21 (2000) 641-650

  47. On periodic billiard trajectories in obtuse triangles (pdf) [abstract] (with Norbert Hungerbühler),
    SIAM Review, 42(4) (2000) 657-670

  48. Dual form of combinatorial problems and Laplace techniques (pdf) [abstract] (with Norbert Hungerbühler),
    The Fibonacci Quarterly, 38 (2000) 395-407

  49. An application of van der Waerden's Theorem in additive number theory (pdf) [abstract] (with Norbert Hungerbühler),
    INTEGERS: The Electronic Journal of Combinatorial Number Theory, 0 (2000) #A07, 5 pages

  50. Can Kirkman's schoolgirls walk abreast by forming arithmetic progressions? (pdf) [abstract],
    The American Mathematical Monthly, 110(3) (2003) 228-231

  51. Fans and bundles in the graph of pairwise sums and products (pdf) [abstract],
    The Electronic Journal of Combinatorics, 11(1) (2004) #R6, 11 pages

  52. Avoiding arithmetic progressions in cyclic groups (pdf) [abstract] (with Stephanie Halbeisen),
    Elemente der Mathematik, 60(3) (2005) 114-123

  53. Minimal generating sets of groups, rings, and fields (pdf) [abstract] (with Martin Hamilton and Pavel Ruzicka),
    Quaestiones Mathematicae, 30(3) (2007) 355-363

  54. A simple proof of Poncelet's theorem (pdf) [abstract] (with Norbert Hungerbühler),
    The American Mathematical Monthly, 122(6) (2015) 537-551

  55. Conjugate conics and closed chains of Poncelet polygons (pdf) [abstract] (with Norbert Hungerbühler),
    Mitteilungen der Mathematischen Gesellschaft in Hamburg, 36 (2016) 5-28

  56. Closed chains of conics carrying Poncelet triangles (pdf) [abstract] (with Norbert Hungerbühler),
    Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 58(2) (2017) 277-302

  57. The exponential pencil of conics (pdf) (with Norbert Hungerbühler),
    Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 59(3) (2018) 549-571

  58. A theorem of Fermat on congruent number curves (pdf) (with Norbert Hungerbühler),
    Hardy-Ramanujan Journal, 41 (2018) 15-21

  59. A geometric representation of integral solutions of x2+xy+y2=m2 (pdf) (with Norbert Hungerbühler),
    Quaestiones Mathematicae, 43(3) (2020) 425-439

  60. An elementary approach to Hessian curves with torsion group ℤ/6ℤ (pdf) (with Norbert Hungerbühler),
    International Electronic Journal of Pure and Applied Mathematics, 13(1) (2019) 1-30

  61. Congruent number elliptic curves related to integral solutions of m2=n2+nl+l2 (pdf) (with Norbert Hungerbühler),
    Journal of Integer Sequences, 22(3) (2019) Article 19.3.1

  62. Heron triangles and their elliptic curves (pdf) (with Norbert Hungerbühler),
    Journal of Number Theory, 213 (2020) 232-253

  63. Sets and multisets of range uniqueness for polynomials (pdf) (with Norbert Hungerbühler and Salome Schumacher),
    Linear Algebra and its Applications, 589 (2020) 39-61

  64. Generalized pencils of conics derived from cubics (pdf) (with Norbert Hungerbühler),
    Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 61(4) (2020) 681-693

  65. Magic sets for polynomials of degree n (pdf) (with Norbert Hungerbühler and Salome Schumacher),
    Linear Algebra and its Applications, 609 (2021) 413-441

  66. On primitive solutions of the diophantine equation x2+y2=M (pdf) (with Chris Busenhart, Norbert Hungerbühler, and Oliver Riesen),
    Open Mathematics, 19(1) (2021) 863-868

  67. Sets of range uniqueness for multivariate polynomials and linear functions with rank k (pdf) (with Norbert Hungerbühler, Salome Schumacher, and Guo Xian Yau),
    Linear and Multilinear Algebra, 70(20) (2022) 5642-5660 (doi)

  68. A family of congruent number elliptic curves of rank three (pdf) (with Norbert Hungerbühler and Arman Shamsi Zargar),
    Quaestiones Mathematicae, 46(6) (2023) 1131-1137 (doi)

  69. Pairing pythagorean pairs (pdf) (with Norbert Hungerbühler),
    Journal of Number Theory, 233 (2022) 467-480 (doi)

  70. Reversion porisms in conics (pdf) (with Norbert Hungerbühler and Marco Schiltknecht),
    International Electronic Journal of Geometry, 14(2) (2021) 371-382 (doi)

  71. A geometric approach to elliptic curves with torsion groups ℤ/10ℤ, ℤ/12ℤ, ℤ/14ℤ, and ℤ/16ℤ (pdf) (with Norbert Hungerbühler, Arman Shamsi Zargar, and Maksym Voznyy),
    Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti 27 (2023) 87-109

  72. Constructing cubic curves with involutions (pdf) (with Norbert Hungerbühler),
    Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 63 (2022) 921-940 (doi)

  73. Configurations on elliptic curves (pdf) (with Andrin Halbeisen and Norbert Hungerbühler),
    Innovations in Incidence Geometry — Algebraic, Topological and Combinatorial, 19(3) (2022) 111-135

  74. Quadrilaterals as geometric loci (pdf) (with Norbert Hungerbühler and Juan Läuchli),
    International Electronic Journal of Geometry 15(2) (2022) 321-333 (doi)

  75. The hidden twin of the Five Circles Theorem (pdf) (with Norbert Hungerbühler and Vanessa Loureiro),
    The American Mathematical Monthly (to appear)

  76. A worked out Galois group for the classroom (pdf) (with Norbert Hungerbühler),
    The American Mathematical Monthly (to appear)

  77. Geometric sums as sums of two squares (pdf) (with Norbert Hungerbühler and Franz Lemmermeyer),
    15 pages, submitted

  78. More configurations on elliptic curves (pdf) (with Marco Bramato and Norbert Hungerbühler),
    14 pages, submitted

  79. Properties of Hesse derivatives of cubic curves (pdf) (with Sayan Dutta and Norbert Hungerbühler),
    14 pages, submitted

  80. Three conics determine a cubic (pdf) (with Norbert Hungerbühler),
    10 pages, submitted

  81. The Pentagon Theorem in Miquelian Möbius planes (pdf) (with Norbert Hungerbühler and Vanessa Loureiro),
    International Electronic Journal of Geometry (to appear)

  82. Building loops with classical Lego train tracks (pdf) (with Norbert Hungerbühler),
    Mathematics Magazine (to appear)

  83. Twins of conic hexagons (pdf) (with Norbert Hungerbühler),
    14 pages, submitted


    84. Philosophical Aspects of Logic and Set Theory

  84. A framework for metamathematics (pdf),
    in Axiomatic Thinking II (Springer Cham, 2022), pages 3-8.


    Solutions to Problems by "The Logic Coffee Circle"

  1. The American Mathematical Monthly: Solution to Problem 12208

  2. The American Mathematical Monthly: Solution to Problem 12224

  3. The American Mathematical Monthly: Solution to Problem 12237

  4. The American Mathematical Monthly: Solution to Problem 12246

  5. The American Mathematical Monthly: Solution to Problem 12256


Résumé de certains travaux (jusqu'en 1999) (pdf)

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Last modified on October 16, 2023