My
Papers
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.

A model in which GCH holds at successors but fails at limits.
Transactions of the American Mathematical Society 329 (1992) 139.
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Strong ultrapowers and long core models.
Journal of Symbolic Logic 58 (1993) 240248.
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Possible behaviours for the Mitchell ordering.
Annals of Pure and Applied Logic 65 (1993) 107123.
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Possible behaviours for the Mitchell ordering II.
Journal of Symbolic Logic 59 (1994) 11961209.
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Coherent sequences versus Radin sequences.
Annals of Pure and Applied Logic 70 (1994) 223241.
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A model in which every Boolean algebra has many subalgebras (with Saharon Shelah)
Journal of Symbolic Logic 60 (1995) 9921004.
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Cardinal invariants above the continuum (with Saharon Shelah).
Annals of Pure and Applied Logic 75 (1995) 251268.
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A consistency result on weak reflection (with Mirna Džamonja and Saharon Shelah).
Fundamenta Mathematicae 148 (1995) 91100 .
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Collapsing successors of singulars.
Proceedings of the American Mathematical Society 125 (1997) 27032709.
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Souslin trees which are hard to specialise.
Proceedings of the American Mathematical Society 125 (1997) 24352441.
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Some independence results on reflection (with Saharon Shelah).
Journal of the London Mathematical Society 59 (1999) 3749.
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The tree property (with Matthew Foreman).
Advances in Mathematics 133 (1998) 132.
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Large cardinal properties of small cardinals (survey)
Proceedings of the 1996 Barcelona Set Theory Meeting, Kluwer (1996), 2339.
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Slides for my talks on Singular Cardinals at the 1998 Luminy Workshop. Provisional version and probably full of mistakes.
Caveat Lector!
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Scales, squares and reflection (with Matthew Foreman and Menachem Magidor)
Journal of Mathematical Logic 1 (2001), no. 1, 3598.
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Canonical structure in the universe of set theory I (with Matthew Foreman and Menachem Magidor)
Annals of Pure and Applied Logic 129 (2004), no. 13, 211243.
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Canonical structure in the universe of set theory II (with Matthew Foreman and Menachem Magidor)
Annals of Pure and Applied Logic 142 (2006) 5575.
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The noncompactness of square (with Matthew Foreman and Menachem Magidor)
Journal of Symbolic Logic 68 (2003), no. 2, 637643.
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Indexed squares (with Ernest Schimmerling)
Israel Journal of Mathematics 131 (2002), 6199.
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A global version of a theorem of BenDavid and Magidor (with Arthur Apter)
Annals of Pure and Applied Logic 102 (2000), no. 3, 199222.
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Identity crises and strong compactness (with Arthur Apter)
Journal of Symbolic Logic 65 (2000), no. 4, 18951910.
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Identity crises II: strong cardinals (with Arthur Apter)
Archive for Mathematical Logic 40 (2001), no. 1, 2538.
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Blowing up the power set of the least measurable (with Arthur Apter)
Journal of Symbolic Logic 67 (2002), no. 3, 915923.
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Diamond and antichains (with Ernest Schimmerling)
Archive for Mathematical Logic 44 (2005) 7176.
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Compactness and incompactness phenomena in set theory
Logic Colloquium '01, 139150, Lecture Notes in Logic 20, Association for Symbolic Logic, Urbana, IL, 2005.
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Notes on singular cardinal combinatorics (survey)
Notre Dame Journal of Formal Logic 46 (2005) 251282.
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Large cardinals with few measures (with Arthur Apter and Joel Hamkins)
Proceedings of the American Mathematical Society 135 (2007) 22912300.
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Some results in polychromatic Ramsey theory (with Uri Abraham and Cliff Smyth)
Journal of Symbolic Logic 72 (2007) 865896.
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The hyperweak distributive law and a related game in Boolean algebras
(with Natasha Dobrinen)
Annals of Pure and Applied Logic 149 (2007) 1424.
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An Llike model containing very large cardinals (with Arthur Apter)
Archive for Mathematical Logic 47 (2008) 6578.
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Iterated forcing and elementary embeddings
To appear in the forthcoming "Handbook of set theory" (ed. Foreman and Kanamori)
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Square on the singular cardinals (with Sy Friedman)
Journal of Symbolic Logic 73 (2008) 13071314.
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Organic and tight (with Matthew Foreman and Ernest Schimmerling)
Annals of Pure and Applied Logic 160 (2009) 2232.
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Diagonal Prikry forcing (with Matthew Foreman)
Journal of Symbolic Logic 75 (2010) 13831402.
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More on full reflection below aleph_omega (with Dorshka Wylie)
Archive for Mathematical Logic 49 (2010) 659671.
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Continuous treelike scales
Central European Journal of Mathematics 8 (2010) 314318.
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Martin's Maximum and weak square (with Menachem Magidor)
Proceedings of the American Mathematical Society 139 (2011) 33393348.
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Graphs containing triangles are not 3common (with Michael Young)
Journal of Combinatorics 2 (2011) 114.
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More results in polychromatic Ramsey theory (with Uri Abraham)
Central European Journal of Mathematics 10 (2012) 10041016.
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A scattering of orders (with Uri Abraham, Robert Bonnet, Mirna Džamonja and Katherine Thompson)
Transactions of the American Mathematical Society 364 (2012) 62596278.
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Singular cardinals and strong extenders (with Arthur Apter and Joel Hamkins)
Central European Journal of Mathematics 11 (2013) 16281634.
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Monochromatic triangles in threecoloured graphs (with Daniel Kráľ, Florian Pfender, Konrad Sperfeld, Andrew Treglown and Michael Young)
Journal of Combinatorial Theory (series B) 103 (2013) 489503.
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Bounded stationary reflection (with Christopher LambieHanson)
Proceedings of the American Mathematical Society 144 (2016) 861873.
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Limits, regularity and removal for finite structures (with Ashwini Aroskar)
To appear in Journal of Symbolic Logic.
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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) 74057441.
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Small universal families of graphs on א_{ω+1} (with Mirna Džamonja and Charles Morgan)
Journal of Symbolic Logic 81 (2016) 541569.
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Collapsing the cardinals of HOD (with Sy Friedman and Mohammad Golshani)
Journal of Mathematical Logic 15 (2015) 1550007.
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The eightfold way (with Sy Friedman, Menachem Magidor, Assaf Rinot and Dima Sinapova)
To appear in Journal of Symbolic Logic.
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Ordinal definable subsets of singular cardinals (with Sy Friedman, Menachem Magidor, Assaf Rinot and Dima Sinapova)
To appear in Israel Journal of Mathematics.
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Dowker and superDowker filters (with Charles Morgan)
To appear in Proceedings of the American Mathematical Society
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Aronszajn and Kurepa trees
To appear in Archive for Mathematical Logic
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Last updated October 23, 2017
URL of this page is http://www.math.cmu.edu/users/jcumming/papers/