My Papers

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  Here are links to various papers. Since 1997 I have been supported by grants from the National Science Foundation. Many of my papers since that date have been based upon work supported by grants 9703945, 0070549, 0400982, 0654046, 1101156 and 1500790.

  1. A model in which GCH holds at successors but fails at limits.
    Transactions of the American Mathematical Society 329 (1992) 1-39.
    DVI file , PostScript file , PDF file .
  2. Strong ultrapowers and long core models.
    Journal of Symbolic Logic 58 (1993) 240-248.
    DVI file , PostScript file , PDF file .
  3. Possible behaviours for the Mitchell ordering.
    Annals of Pure and Applied Logic 65 (1993) 107-123.
    DVI file , PostScript file , PDF file .
  4. Possible behaviours for the Mitchell ordering II.
    Journal of Symbolic Logic 59 (1994) 1196-1209.
    DVI file , PostScript file , PDF file .
  5. Coherent sequences versus Radin sequences.
    Annals of Pure and Applied Logic 70 (1994) 223-241.
    DVI file , PostScript file , PDF file .
  6. A model in which every Boolean algebra has many subalgebras (with Saharon Shelah)
    Journal of Symbolic Logic 60 (1995) 992-1004.
    DVI file , PostScript file , PDF file .
  7. Cardinal invariants above the continuum (with Saharon Shelah).
    Annals of Pure and Applied Logic 75 (1995) 251-268.
    DVI file , PostScript file , PDF file .
  8. A consistency result on weak reflection (with Mirna Džamonja and Saharon Shelah).
    Fundamenta Mathematicae 148 (1995) 91-100 .
    DVI file , PostScript file , PDF file .
  9. Collapsing successors of singulars.
    Proceedings of the American Mathematical Society 125 (1997) 2703-2709.
    DVI file , PostScript file , PDF file .
  10. Souslin trees which are hard to specialise.
    Proceedings of the American Mathematical Society 125 (1997) 2435-2441.
    DVI file , PostScript file , PDF file .
  11. Some independence results on reflection (with Saharon Shelah).
    Journal of the London Mathematical Society 59 (1999) 37-49.
    DVI file , PostScript file , PDF file .
  12. The tree property (with Matthew Foreman).
    Advances in Mathematics 133 (1998) 1-32.
    DVI file , PostScript file , PDF file .
  13. Large cardinal properties of small cardinals (survey)
    Proceedings of the 1996 Barcelona Set Theory Meeting, Kluwer (1996), 23-39.
    DVI file , PostScript file . PDF file .
  14. Slides for my talks on Singular Cardinals at the 1998 Luminy Workshop. Provisional version and probably full of mistakes.
    Caveat Lector!
    DVI file , PostScript file , PDF file .
  15. Scales, squares and reflection (with Matthew Foreman and Menachem Magidor)
    Journal of Mathematical Logic 1 (2001), no. 1, 35--98.
    DVI file , PostScript file , PDF file .
  16. Canonical structure in the universe of set theory I (with Matthew Foreman and Menachem Magidor)
    Annals of Pure and Applied Logic 129 (2004), no. 1-3, 211--243.
    DVI file , PostScript file , PDF file .
  17. Canonical structure in the universe of set theory II (with Matthew Foreman and Menachem Magidor)
    Annals of Pure and Applied Logic 142 (2006) 55--75.
    DVI file , PostScript file , PDF file .
  18. The non-compactness of square (with Matthew Foreman and Menachem Magidor)
    Journal of Symbolic Logic 68 (2003), no. 2, 637--643.
    DVI file , PostScript file , PDF file .
  19. Indexed squares (with Ernest Schimmerling)
    Israel Journal of Mathematics 131 (2002), 61--99.
    DVI file , PostScript file , PDF file .
  20. A global version of a theorem of Ben-David and Magidor (with Arthur Apter)
    Annals of Pure and Applied Logic 102 (2000), no. 3, 199--222.
    DVI file , PostScript file , PDF file .
  21. Identity crises and strong compactness (with Arthur Apter)
    Journal of Symbolic Logic 65 (2000), no. 4, 1895--1910.
    DVI file , PostScript file , PDF file .
  22. Identity crises II: strong cardinals (with Arthur Apter)
    Archive for Mathematical Logic 40 (2001), no. 1, 25--38.
    DVI file , PostScript file , PDF file .
  23. Blowing up the power set of the least measurable (with Arthur Apter)
    Journal of Symbolic Logic 67 (2002), no. 3, 915--923.
    DVI file , PostScript file , PDF file .
  24. Diamond and antichains (with Ernest Schimmerling)
    Archive for Mathematical Logic 44 (2005) 71--76.
    DVI file , PostScript file , PDF file .
  25. Compactness and incompactness phenomena in set theory
    Logic Colloquium '01, 139--150, Lecture Notes in Logic 20, Association for Symbolic Logic, Urbana, IL, 2005.
    DVI file , PostScript file , PDF file .
  26. Notes on singular cardinal combinatorics (survey)
    Notre Dame Journal of Formal Logic 46 (2005) 251--282.
    PDF file .
  27. Large cardinals with few measures (with Arthur Apter and Joel Hamkins)
    Proceedings of the American Mathematical Society 135 (2007) 2291--2300.
    DVI file , PDF file .
  28. Some results in polychromatic Ramsey theory (with Uri Abraham and Cliff Smyth)
    Journal of Symbolic Logic 72 (2007) 865--896.
    PDF file .
  29. The hyper-weak distributive law and a related game in Boolean algebras (with Natasha Dobrinen)
    Annals of Pure and Applied Logic 149 (2007) 14--24.
    PDF file .
  30. An L-like model containing very large cardinals (with Arthur Apter)
    Archive for Mathematical Logic 47 (2008) 65--78.
    PDF file .
  31. Iterated forcing and elementary embeddings
    To appear in the forthcoming "Handbook of set theory" (ed. Foreman and Kanamori)
    PDF file .
  32. Square on the singular cardinals (with Sy Friedman)
    Journal of Symbolic Logic 73 (2008) 1307-1314.
    PDF file .
  33. Organic and tight (with Matthew Foreman and Ernest Schimmerling)
    Annals of Pure and Applied Logic 160 (2009) 22-32.
    PDF file .
  34. Diagonal Prikry forcing (with Matthew Foreman)
    Journal of Symbolic Logic 75 (2010) 1383-1402.
    PDF file .
  35. More on full reflection below aleph_omega (with Dorshka Wylie)
    Archive for Mathematical Logic 49 (2010) 659-671.
    PDF file .
  36. Continuous tree-like scales
    Central European Journal of Mathematics 8 (2010) 314-318.
    PDF file .
  37. Martin's Maximum and weak square (with Menachem Magidor)
    Proceedings of the American Mathematical Society 139 (2011) 3339-3348.
    PDF file .
  38. Graphs containing triangles are not 3-common (with Michael Young)
    Journal of Combinatorics 2 (2011) 1-14.
    PDF file .
  39. More results in polychromatic Ramsey theory (with Uri Abraham)
    Central European Journal of Mathematics 10 (2012) 1004-1016.
    PDF file .
  40. A scattering of orders (with Uri Abraham, Robert Bonnet, Mirna Džamonja and Katherine Thompson)
    Transactions of the American Mathematical Society 364 (2012) 6259-6278.
    PDF file .
  41. Singular cardinals and strong extenders (with Arthur Apter and Joel Hamkins)
    Central European Journal of Mathematics 11 (2013) 1628-1634.
    PDF file .
  42. Monochromatic triangles in three-coloured graphs (with Daniel Kráľ, Florian Pfender, Konrad Sperfeld, Andrew Treglown and Michael Young)
    Journal of Combinatorial Theory (series B) 103 (2013) 489-503.
    PDF file .
  43. Bounded stationary reflection (with Christopher Lambie-Hanson)
    Proceedings of the American Mathematical Society 144 (2016) 861-873.
    PDF file .
  44. Limits, regularity and removal for finite structures (with Ashwini Aroskar)
    To appear in Journal of Symbolic Logic.
    PDF file .
  45. A framework for forcing constructions at successors of singular cardinals (with Mirna Džamonja, Menachem Magidor, Charles Morgan and Saharon Shelah)
    Transactions of the American Mathematical Society 369 (2017) 7405-7441.
    PDF file .
  46. Small universal families of graphs on אω+1 (with Mirna Džamonja and Charles Morgan)
    Journal of Symbolic Logic 81 (2016) 541-569.
    PDF file .
  47. Collapsing the cardinals of HOD (with Sy Friedman and Mohammad Golshani)
    Journal of Mathematical Logic 15 (2015) 1550007.
    PDF file .
  48. The eightfold way (with Sy Friedman, Menachem Magidor, Assaf Rinot and Dima Sinapova)
    To appear in Journal of Symbolic Logic.
    PDF file .
  49. Ordinal definable subsets of singular cardinals (with Sy Friedman, Menachem Magidor, Assaf Rinot and Dima Sinapova)
    To appear in Israel Journal of Mathematics.
    PDF file .
  50. Dowker and super-Dowker filters (with Charles Morgan)
    To appear in Proceedings of the American Mathematical Society
    PDF file .
  51. Aronszajn and Kurepa trees
    To appear in Archive for Mathematical Logic
    PDF file .
Last updated October 23, 2017
URL of this page is http://www.math.cmu.edu/users/jcumming/papers/