# Large cardinal publications

• Nonlinearity in the hierarchy of large cardinal consistency strength

This is currently a draft version only of my article-in-progress on the topic of linearity in the hierarchy of consistency strength, especially with large cardinals. Comments are very welcome, since I am still writing the article. Please kindly send me …

• Categorical large cardinals and the tension between categoricity and set-theoretic reflection
• J. D. Hamkins and R. Solberg, “Categorical large cardinals and the tension between categoricity and set-theoretic reflection,” Mathematics arXiv, 2020. (Under review)
@ARTICLE{HamkinsSolberg:Categorical-large-cardinals,
author = {Joel David Hamkins and Robin Solberg},
title = {Categorical large cardinals and the tension between categoricity and set-theoretic reflection},
journal = {Mathematics arXiv},
year = {2020},
volume = {},
number = {},
pages = {},
month = {},
note = {Under review},
abstract = {},
keywords = {under-review},
url = {http://jdh.hamkins.org/categorical-large-cardinals/},
source = {},
doi = {},
eprint = {2009.07164},
archivePrefix ={arXiv},
primaryClass = {math.LO}
}

• The Vopěnka principle is inequivalent to but conservative over the Vopěnka scheme
• J. D. Hamkins, “The Vopěnka principle is inequivalent to but conservative over the Vopěnka scheme,” ArXiv e-prints, 2016. (Under review)
@ARTICLE{Hamkins:The-Vopenka-principle-is-inequivalent-to-but-conservative-over-the-Vopenka-scheme,
author = {Joel David Hamkins},
title = {The {Vop\v{e}nka} principle is inequivalent to but conservative over the {Vop\v{e}nka} scheme},
journal = {ArXiv e-prints},
year = {2016},
volume = {},
number = {},
pages = {},
month = {},
note = {Under review},
abstract = {},
keywords = {under-review},
source = {},
eprint = {1606.03778},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://wp.me/p5M0LV-1lV},
}

• Large cardinals need not be large in HOD
• Y. Cheng, S. Friedman, and J. D. Hamkins, “Large cardinals need not be large in HOD,” Annals of Pure and Applied Logic, vol. 166, iss. 11, pp. 1186-1198, 2015.
@ARTICLE{ChengFriedmanHamkins2015:LargeCardinalsNeedNotBeLargeInHOD,
title = "Large cardinals need not be large in {HOD} ",
journal = "Annals of Pure and Applied Logic ",
volume = "166",
number = "11",
pages = "1186 - 1198",
year = "2015",
note = "",
issn = "0168-0072",
doi = "10.1016/j.apal.2015.07.004",
eprint = {1407.6335},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://jdh.hamkins.org/large-cardinals-need-not-be-large-in-hod},
author = "Yong Cheng and Sy-David Friedman and Joel David Hamkins",
keywords = "Large cardinals",
keywords = "HOD",
keywords = "Forcing",
keywords = "Absoluteness ",
abstract = "Abstract We prove that large cardinals need not generally exhibit their large cardinal nature in HOD. For example, a supercompact cardinal κ need not be weakly compact in HOD, and there can be a proper class of supercompact cardinals in V, none of them weakly compact in HOD, with no supercompact cardinals in HOD. Similar results hold for many other types of large cardinals, such as measurable and strong cardinals.",
}

• Strongly uplifting cardinals and the boldface resurrection axioms
• J. D. Hamkins and T. Johnstone, “Strongly uplifting cardinals and the boldface resurrection axioms,” Archive for Mathematical Logic, vol. 56, iss. 7, pp. 1115-1133, 2017.
@ARTICLE{HamkinsJohnstone2017:StronglyUpliftingCardinalsAndBoldfaceResurrection,
author = {Joel David Hamkins and Thomas Johnstone},
title = {Strongly uplifting cardinals and the boldface resurrection axioms},
journal="Archive for Mathematical Logic",
year="2017",
month="Nov",
day="01",
volume="56",
number="7",
pages="1115--1133",
eprint = {1403.2788},
archivePrefix = {arXiv},
primaryClass = {math.LO},
issn="1432-0665",
doi="10.1007/s00153-017-0542-y",
url = {http://wp.me/p5M0LV-IE},
abstract="We introduce the strongly uplifting cardinals, which are equivalently characterized, we prove, as the superstrongly unfoldable cardinals and also as the almost-hugely unfoldable cardinals, and we show that their existence is equiconsistent over ZFC with natural instances of the boldface resurrection axiom, such as the boldface resurrection axiom for proper forcing.",
keywords = {},
source = {},
}

• Resurrection axioms and uplifting cardinals
• J. D. Hamkins and T. Johnstone, “Resurrection axioms and uplifting cardinals,” Archive for Mathematical Logic, vol. 53, iss. 3-4, p. p.~463–485, 2014.
@ARTICLE{HamkinsJohnstone2014:ResurrectionAxiomsAndUpliftingCardinals,
AUTHOR = "Joel David Hamkins and Thomas Johnstone",
TITLE = "Resurrection axioms and uplifting cardinals",
JOURNAL = "Archive for Mathematical Logic",
publisher= {Springer},
YEAR = "2014",
volume = "53",
number = "3-4",
pages = "p.~463--485",
month = "",
note = "",
url = "http://jdh.hamkins.org/resurrection-axioms-and-uplifting-cardinals",
eprint = "1307.3602",
archivePrefix = {arXiv},
primaryClass = {math.LO},
doi= "10.1007/s00153-014-0374-y",
issn= {0933-5846},
abstract = "",
keywords = "",
source = "",
file = F,
}

• Superstrong and other large cardinals are never Laver indestructible
• J. Bagaria, J. D. Hamkins, K. Tsaprounis, and T. Usuba, “Superstrong and other large cardinals are never Laver indestructible,” Arch. Math. Logic, vol. 55, iss. 1-2, pp. 19-35, 2016. (Special volume in memory of R.~Laver)
@ARTICLE{BagariaHamkinsTsaprounisUsuba2016:SuperstrongAndOtherLargeCardinalsAreNeverLaverIndestructible,
AUTHOR = {Bagaria, Joan and Hamkins, Joel David and Tsaprounis,
Konstantinos and Usuba, Toshimichi},
TITLE = {Superstrong and other large cardinals are never {L}aver
indestructible},
JOURNAL = {Arch. Math. Logic},
FJOURNAL = {Archive for Mathematical Logic},
note = {Special volume in memory of R.~Laver},
VOLUME = {55},
YEAR = {2016},
NUMBER = {1-2},
PAGES = {19--35},
ISSN = {0933-5846},
MRCLASS = {03E55 (03E40)},
MRNUMBER = {3453577},
MRREVIEWER = {Peter Holy},
DOI = {10.1007/s00153-015-0458-3},
eprint = {1307.3486},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://jdh.hamkins.org/superstrong-never-indestructible/},
}

• The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $\theta$-supercompact
• B. Cody, M. Gitik, J. D. Hamkins, and J. A. Schanker, “The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $\theta$ supercompact,” Archive for Mathematical Logic, pp. 1-20, 2015.
@article{CodyGitikHamkinsSchanker2015:LeastWeaklyCompact,
year= {2015},
issn= {0933-5846},
journal= {Archive for Mathematical Logic},
doi= {10.1007/s00153-015-0423-1},
title= {The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $\theta$ supercompact},
publisher= {Springer},
keywords= {Weakly compact; Unfoldable; Weakly measurable; Nearly supercompact; Identity crisis; Primary 03E55; 03E35},
author= {Cody, Brent and Gitik, Moti and Hamkins, Joel David and Schanker, Jason A.},
pages= {1--20},
language= {English},
eprint = {1305.5961},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url= {http://jdh.hamkins.org/least-weakly-compact},
}

• A multiverse perspective on the axiom of constructiblity
• J. D. Hamkins, “A multiverse perspective on the axiom of constructibility,” in Infinity and Truth, World Sci. Publ., Hackensack, NJ, 2014, vol. 25, pp. 25-45.
@incollection {Hamkins2014:MultiverseOnVeqL,
AUTHOR = {Hamkins, Joel David},
TITLE = {A multiverse perspective on the axiom of constructibility},
BOOKTITLE = {{Infinity and Truth}},
SERIES = {LNS Math Natl. Univ. Singap.},
VOLUME = {25},
PAGES = {25--45},
PUBLISHER = {World Sci. Publ., Hackensack, NJ},
YEAR = {2014},
MRCLASS = {03E45 (03A05)},
MRNUMBER = {3205072},
DOI = {10.1142/9789814571043_0002},
url = {http://wp.me/p5M0LV-qE},
eprint = {1210.6541},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• Moving up and down in the generic multiverse
• J. D. Hamkins and B. Löwe, “Moving up and down in the generic multiverse,” Logic and its Applications, ICLA 2013 LNCS, vol. 7750, pp. 139-147, 2013.
@ARTICLE{HamkinsLoewe2013:MovingUpAndDownInTheGenericMultiverse,
AUTHOR = {Joel David Hamkins and Benedikt Löwe},
title = {Moving up and down in the generic multiverse},
journal = {Logic and its Applications, ICLA 2013 LNCS},
publisher= {Springer},
editor= {Lodaya, Kamal},
isbn= {978-3-642-36038-1},
year = {2013},
volume = {7750},
number = {},
pages = {139--147},
doi= {10.1007/978-3-642-36039-8_13},
month = {},
note = {},
url = {http://wp.me/p5M0LV-od},
eprint = {1208.5061},
archivePrefix = {arXiv},
primaryClass = {math.LO},
abstract = {},
keywords = {},
source = {},
}

• Well-founded Boolean ultrapowers as large cardinal embeddings
• J. D. Hamkins and D. Seabold, “Well-founded Boolean ultrapowers as large cardinal embeddings,” , pp. 1-40, 2006.
@ARTICLE{HamkinsSeabold:BooleanUltrapowers,
AUTHOR = "Joel David Hamkins and Daniel Seabold",
TITLE = "Well-founded {Boolean} ultrapowers as large cardinal embeddings",
JOURNAL = "",
YEAR = "2006",
volume = "",
number = "",
pages = "1--40",
month = "",
note = "",
eprint = "1206.6075",
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://jdh.hamkins.org/boolean-ultrapowers/},
abstract = "",
keywords = "",
source = "",
file = F,
}

• Singular cardinals and strong extenders
• A. W. Apter, J. Cummings, and J. D. Hamkins, “Singular cardinals and strong extenders,” Central European Journal of Mathematics, vol. 11, iss. 9, pp. 1628-1634, 2013.
@article {ApterCummingsHamkins2013:SingularCardinalsAndStrongExtenders,
AUTHOR = {Apter, Arthur W. and Cummings, James and Hamkins, Joel David},
TITLE = {Singular cardinals and strong extenders},
JOURNAL = {Central European Journal of Mathematics},
VOLUME = {11},
YEAR = {2013},
NUMBER = {9},
PAGES = {1628--1634},
ISSN = {1895-1074},
MRCLASS = {03E55 (03E35 03E45)},
MRNUMBER = {3071929},
MRREVIEWER = {Samuel Gomes da Silva},
DOI = {10.2478/s11533-013-0265-1},
URL = {http://jdh.hamkins.org/singular-cardinals-strong-extenders/},
eprint = {1206.3703},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• Inner models with large cardinal features usually obtained by forcing
• A. W.~Apter, V. Gitman, and J. D. Hamkins, “Inner models with large cardinal features usually obtained by forcing,” Archive for Math.~Logic, vol. 51, pp. 257-283, 2012.
@article {ApterGitmanHamkins2012:InnerModelsWithLargeCardinals,
author = {Arthur W.~Apter and Victoria Gitman and Joel David Hamkins},
affiliation = {Mathematics, The Graduate Center of the City University of New York, 365 Fifth Avenue, New York, NY 10016, USA},
title = {Inner models with large cardinal features usually obtained by forcing},
journal = {Archive for Math.~Logic},
publisher = {Springer},
issn = {0933-5846},
keyword = {},
pages = {257--283},
volume = {51},
issue = {3},
url = {http://jdh.hamkins.org/innermodels},
eprint = {1111.0856},
archivePrefix = {arXiv},
primaryClass = {math.LO},
doi = {10.1007/s00153-011-0264-5},
note = {},
year = {2012},
}

• What is the theory ZFC without power set?
• V. Gitman, J. D. Hamkins, and T. A.~Johnstone, “What is the theory ZFC without Powerset?,” Math.~Logic Q., vol. 62, iss. 4–5, pp. 391-406, 2016.
@ARTICLE{GitmanHamkinsJohnstone2016:WhatIsTheTheoryZFC-Powerset?,
AUTHOR = {Victoria Gitman and Joel David Hamkins and Thomas A.~Johnstone},
TITLE = {What is the theory {ZFC} without {Powerset}?},
JOURNAL = {Math.~Logic Q.},
YEAR = {2016},
volume = {62},
number = {4--5},
pages = {391--406},
month = {},
note = {},
abstract = {},
keywords = {},
doi = {10.1002/malq.201500019},
eprint = {1110.2430},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://jdh.hamkins.org/what-is-the-theory-zfc-without-power-set},
source = {},
ISSN = {0942-5616},
MRCLASS = {03E30},
MRNUMBER = {3549557},
MRREVIEWER = {Arnold W. Miller},
}

• Generalizations of the Kunen inconsistency
• J. D. Hamkins, G. Kirmayer, and N. L. Perlmutter, “Generalizations of the Kunen inconsistency,” Annals of Pure and Applied Logic, vol. 163, iss. 12, pp. 1872-1890, 2012.
@article{HamkinsKirmayerPerlmutter2012:GeneralizationsOfKunenInconsistency,
title = "Generalizations of the {Kunen} inconsistency",
journal = "Annals of Pure and Applied Logic",
volume = "163",
number = "12",
pages = "1872 - 1890",
year = "2012",
note = "",
issn = "0168-0072",
doi = "10.1016/j.apal.2012.06.001",
eprint = {1106.1951},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = "http://jdh.hamkins.org/generalizationsofkuneninconsistency",
author = "Joel David Hamkins and Greg Kirmayer and Norman Lewis Perlmutter",
}

• Indestructible strong unfoldability
• J. D. Hamkins and T. A. Johnstone, “Indestructible strong unfoldability,” Notre Dame Journal of Formal Logic, vol. 51, iss. 3, pp. 291-321, 2010.
@ARTICLE{HamkinsJohnstone2010:IndestructibleStrongUnfoldability,
AUTHOR = {Hamkins, Joel David and Johnstone, Thomas A.},
TITLE = {Indestructible strong unfoldability},
JOURNAL = {Notre Dame Journal of Formal Logic},
FJOURNAL = {Notre Dame Journal of Formal Logic},
VOLUME = {51},
YEAR = {2010},
NUMBER = {3},
PAGES = {291--321},
ISSN = {0029-4527},
MRCLASS = {03E55 (03E40)},
MRNUMBER = {2675684 (2011i:03050)},
MRREVIEWER = {Bernhard A. König},
DOI = {10.1215/00294527-2010-018},
URL = {http://jdh.hamkins.org/indestructiblestrongunfoldability/},
file = F,
}

• Tall cardinals
• J. D. Hamkins, “Tall cardinals,” Math.~Logic Q., vol. 55, iss. 1, pp. 68-86, 2009.
@ARTICLE{Hamkins2009:TallCardinals,
AUTHOR = {Hamkins, Joel D.},
TITLE = {Tall cardinals},
JOURNAL = {Math.~Logic Q.},
FJOURNAL = {Mathematical Logic Quarterly},
VOLUME = {55},
YEAR = {2009},
NUMBER = {1},
PAGES = {68--86},
ISSN = {0942-5616},
MRCLASS = {03E55 (03E35)},
MRNUMBER = {2489293 (2010g:03083)},
MRREVIEWER = {Carlos A.~Di Prisco},
DOI = {10.1002/malq.200710084},
URL = {http://wp.me/p5M0LV-3y},
file = F,
}

• The proper and semi-proper forcing axioms for forcing notions that preserve $\aleph_2$ or $\aleph_3$
• J. D. Hamkins and T. A. Johnstone, “The proper and semi-proper forcing axioms for forcing notions that preserve $\aleph_2$ or $\aleph_3$,” Proc.~Amer.~Math.~Soc., vol. 137, iss. 5, pp. 1823-1833, 2009.
@ARTICLE{HamkinsJohnstone2009:PFA(aleph_2-preserving),
AUTHOR = {Hamkins, Joel David and Johnstone, Thomas A.},
TITLE = {The proper and semi-proper forcing axioms for forcing notions that preserve {$\aleph_2$} or {$\aleph_3$}},
JOURNAL = {Proc.~Amer.~Math.~Soc.},
FJOURNAL = {Proceedings of the American Mathematical Society},
VOLUME = {137},
YEAR = {2009},
NUMBER = {5},
PAGES = {1823--1833},
ISSN = {0002-9939},
CODEN = {PAMYAR},
MRCLASS = {03E55 (03E40)},
MRNUMBER = {2470843 (2009k:03087)},
MRREVIEWER = {John Krueger},
DOI = {10.1090/S0002-9939-08-09727-X},
URL = {http://wp.me/p5M0LV-3v},
file = F,
}

• Large cardinals with few measures
• A. W.~Apter, J. Cummings, and J. D. Hamkins, “Large cardinals with few measures,” Proc.~Amer.~Math.~Soc., vol. 135, iss. 7, pp. 2291-2300, 2007.
@ARTICLE{ApterCummingsHamkins2006:LargeCardinalsWithFewMeasures,
AUTHOR = {Arthur W.~Apter and James Cummings and Joel David Hamkins},
TITLE = {Large cardinals with few measures},
JOURNAL = {Proc.~Amer.~Math.~Soc.},
FJOURNAL = {Proceedings of the American Mathematical Society},
VOLUME = {135},
YEAR = {2007},
NUMBER = {7},
PAGES = {2291--2300},
ISSN = {0002-9939},
CODEN = {PAMYAR},
MRCLASS = {03E35 (03E55)},
MRNUMBER = {2299507 (2008b:03067)},
MRREVIEWER = {Tetsuya Ishiu},
DOI = {10.1090/S0002-9939-07-08786-2},
URL = {http://jdh.hamkins.org/largecardinalswithfewmeasures/},
eprint = {math/0603260},
archivePrefix = {arXiv},
primaryClass = {math.LO},
file = F,
}

• Extensions with the approximation and cover properties have no new large cardinals
• J. D. Hamkins, “Extensions with the approximation and cover properties have no new large cardinals,” Fund.~Math., vol. 180, iss. 3, pp. 257-277, 2003.
@article{Hamkins2003:ExtensionsWithApproximationAndCoverProperties,
AUTHOR = {Hamkins, Joel David},
TITLE = {Extensions with the approximation and cover properties have no new large cardinals},
JOURNAL = {Fund.~Math.},
FJOURNAL = {Fundamenta Mathematicae},
VOLUME = {180},
YEAR = {2003},
NUMBER = {3},
PAGES = {257--277},
ISSN = {0016-2736},
MRCLASS = {03E55 (03E40)},
MRNUMBER = {2063629 (2005m:03100)},
DOI = {10.4064/fm180-3-4},
URL = {http://wp.me/p5M0LV-2B},
eprint = {math/0307229},
archivePrefix = {arXiv},
primaryClass = {math.LO},
file = F,
}

• Exactly controlling the non-supercompact strongly compact cardinals
• A. W.~Apter and J. D. Hamkins, “Exactly controlling the non-supercompact strongly compact cardinals,” Journal of Symbolic Logic, vol. 68, iss. 2, pp. 669-688, 2003.
@ARTICLE{ApterHamkins2003:ExactlyControlling,
AUTHOR = {Arthur W.~Apter and Joel David Hamkins},
TITLE = {Exactly controlling the non-supercompact strongly compact cardinals},
JOURNAL = {Journal of Symbolic Logic},
VOLUME = {68},
YEAR = {2003},
NUMBER = {2},
PAGES = {669--688},
ISSN = {0022-4812},
CODEN = {JSYLA6},
MRCLASS = {03E35 (03E55)},
MRNUMBER = {1976597 (2004b:03075)},
MRREVIEWER = {A.~Kanamori},
doi = {10.2178/jsl/1052669070},
eprint = {math/0301016},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://wp.me/p5M0LV-2x},
}

• A simple maximality principle
• J. D. Hamkins, “A simple maximality principle,” Journal of Symbolic Logic, vol. 68, iss. 2, pp. 527-550, 2003.
@article{Hamkins2003:MaximalityPrinciple,
AUTHOR = {Hamkins, Joel David},
TITLE = {A simple maximality principle},
JOURNAL = {Journal of Symbolic Logic},
VOLUME = {68},
YEAR = {2003},
NUMBER = {2},
PAGES = {527--550},
ISSN = {0022-4812},
CODEN = {JSYLA6},
MRCLASS = {03E35 (03E40)},
MRNUMBER = {1976589 (2005a:03094)},
MRREVIEWER = {Ralf-Dieter Schindler},
DOI = {10.2178/jsl/1052669062},
URL = {http://wp.me/p5M0LV-2v},
month = {},
eprint = {math/0009240},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• Indestructibility and the level-by-level agreement between strong compactness and supercompactness
• A. W.~Apter and J. D. Hamkins, “Indestructibility and the level-by-level agreement between strong compactness and supercompactness,” Journal of Symbolic Logic, vol. 67, iss. 2, pp. 820-840, 2002.
@ARTICLE{ApterHamkins2002:LevelByLevel,
AUTHOR = {Arthur W.~Apter and Joel David Hamkins},
TITLE = {Indestructibility and the level-by-level agreement between strong compactness and supercompactness},
JOURNAL = {Journal of Symbolic Logic},
VOLUME = {67},
YEAR = {2002},
NUMBER = {2},
PAGES = {820--840},
ISSN = {0022-4812},
CODEN = {JSYLA6},
MRCLASS = {03E35 (03E55)},
MRNUMBER = {1905168 (2003e:03095)},
MRREVIEWER = {Carlos A.~Di Prisco},
DOI = {10.2178/jsl/1190150111},
URL = {http://wp.me/p5M0LV-2i},
eprint = {math/0102086},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata
• A. W.~Apter and J. D. Hamkins, “Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata,” Math.~Logic Q., vol. 47, iss. 4, pp. 563-571, 2001.
@ARTICLE{ApterHamkins2001:IndestructibleWC,
AUTHOR = {Arthur W.~Apter and Joel David Hamkins},
TITLE = {Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata},
JOURNAL = {Math.~Logic Q.},
FJOURNAL = {Mathematical Logic Quarterly},
VOLUME = {47},
YEAR = {2001},
NUMBER = {4},
PAGES = {563--571},
ISSN = {0942-5616},
MRCLASS = {03E35 (03E55)},
MRNUMBER = {1865776 (2003h:03078)},
DOI = {10.1002/1521-3870(200111)47:4%3C563::AID-MALQ563%3E3.0.CO;2-%23},
URL = {http://jdh.hamkins.org/indestructiblewc/},
eprint = {math/9907046},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• The wholeness axioms and $V=\rm HOD$
• J. D. Hamkins, “The wholeness axioms and $V=\rm HOD$,” Arch.~Math.~Logic, vol. 40, iss. 1, pp. 1-8, 2001.
@article{Hamkins2001:WholenessAxiom,
AUTHOR = {Hamkins, Joel David},
TITLE = {The wholeness axioms and {$V=\rm HOD$}},
JOURNAL = {Arch.~Math.~Logic},
FJOURNAL = {Archive for Mathematical Logic},
VOLUME = {40},
YEAR = {2001},
NUMBER = {1},
PAGES = {1--8},
ISSN = {0933-5846},
CODEN = {AMLOEH},
MRCLASS = {03E35 (03E65)},
MRNUMBER = {1816602 (2001m:03102)},
MRREVIEWER = {Ralf-Dieter Schindler},
DOI = {10.1007/s001530050169},
URL = {http://wp.me/p5M0LV-1k},
eprint = {math/9902079},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• The lottery preparation
• J. D. Hamkins, “The lottery preparation,” Ann.~Pure Appl.~Logic, vol. 101, iss. 2-3, pp. 103-146, 2000.
@article {Hamkins2000:LotteryPreparation,
AUTHOR = {Hamkins, Joel David},
TITLE = {The lottery preparation},
JOURNAL = {Ann.~Pure Appl.~Logic},
FJOURNAL = {Annals of Pure and Applied Logic},
VOLUME = {101},
YEAR = {2000},
NUMBER = {2-3},
PAGES = {103--146},
ISSN = {0168-0072},
CODEN = {APALD7},
MRCLASS = {03E55 (03E40)},
MRNUMBER = {1736060 (2001i:03108)},
MRREVIEWER = {Klaas Pieter Hart},
DOI = {10.1016/S0168-0072(99)00010-X},
URL = {http://jdh.hamkins.org/lotterypreparation/},
eprint = {math/9808012},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• Book review of The Higher Infinite, Akihiro Kanamori
• J. D. Hamkins, “book review of The Higher Infinite, Akihiro Kanamori,” Studia Logica, vol. 65, iss. 3, pp. 443-446, 2000.
@ARTICLE{Hamkins2000:BookReviewKanamori,
AUTHOR = "Joel David Hamkins",
TITLE = "book review of {The Higher Infinite, Akihiro Kanamori}",
JOURNAL = "Studia Logica",
publisher = "Springer Netherlands",
YEAR = "2000",
volume = "65",
number = "3",
pages = "443--446",
month = "",
note = "",
abstract = "",
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• Gap forcing: generalizing the Lévy-Solovay theorem
• J. D. Hamkins, “Gap forcing: generalizing the Lévy-Solovay theorem,” Bulletin of Symbolic Logic, vol. 5, iss. 2, pp. 264-272, 1999.
@article{Hamkins99:GapForcingGen,
AUTHOR = {Hamkins, Joel David},
TITLE = {Gap forcing: generalizing the {L}\'evy-{S}olovay theorem},
JOURNAL = {Bulletin of Symbolic Logic},
FJOURNAL = {The Bulletin of Symbolic Logic},
VOLUME = {5},
YEAR = {1999},
NUMBER = {2},
PAGES = {264--272},
ISSN = {1079-8986},
MRCLASS = {03E40 (03E55)},
MRNUMBER = {1792281 (2002g:03106)},
MRREVIEWER = {Carlos A.~Di Prisco},
DOI = {10.2307/421092},
URL = {http://jdh.hamkins.org/gapforcinggen/},
month = {June},
eprint = {math/9901108},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• Universal indestructibility
• A. W.~Apter and J. D. Hamkins, “Universal indestructibility,” Kobe Journal of Mathematics, vol. 16, iss. 2, pp. 119-130, 1999.
@article {ApterHamkins99:UniversalIndestructibility,
AUTHOR = {Arthur W.~Apter and Joel David Hamkins},
TITLE = {Universal indestructibility},
JOURNAL = {Kobe Journal of Mathematics},
VOLUME = {16},
YEAR = {1999},
NUMBER = {2},
PAGES = {119--130},
ISSN = {0289-9051},
MRCLASS = {03E55 (03E35)},
MRNUMBER = {1745027 (2001k:03112)},
MRNUMBER = {1 745 027},
eprint = {math/9808004},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://wp.me/p5M0LV-12},
}

• Superdestructibility: a dual to Laver's indestructibility
• J. D. Hamkins and S. Shelah, “Superdestructibility: a dual to Laver’s indestructibility,” Journal of Symbolic Logic, vol. 63, iss. 2, pp. 549-554, 1998. ([HmSh:618])
@article {HamkinsShelah98:Dual,
AUTHOR = {Hamkins, Joel David and Shelah, Saharon},
TITLE = {Superdestructibility: a dual to {L}aver's indestructibility},
JOURNAL = {Journal of Symbolic Logic},
VOLUME = {63},
YEAR = {1998},
NUMBER = {2},
PAGES = {549--554},
ISSN = {0022-4812},
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MRCLASS = {03E55 (03E40)},
MRNUMBER = {1625927 (99m:03106)},
MRREVIEWER = {Douglas R.~Burke},
DOI = {10.2307/2586848},
URL = {http://jdh.hamkins.org/dual/},
note = {[HmSh:618]},
eprint = {math/9612227},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• Small forcing makes any cardinal superdestructible
• J. D. Hamkins, “Small forcing makes any cardinal superdestructible,” Journal of Symbolic Logic, vol. 63, iss. 1, pp. 51-58, 1998.
@article {Hamkins98:SmallForcing,
AUTHOR = {Hamkins, Joel David},
TITLE = {Small forcing makes any cardinal superdestructible},
JOURNAL = {Journal of Symbolic Logic},
VOLUME = {63},
YEAR = {1998},
NUMBER = {1},
PAGES = {51--58},
ISSN = {0022-4812},
CODEN = {JSYLA6},
MRCLASS = {03E40 (03E55)},
MRNUMBER = {1607499 (99b:03068)},
MRREVIEWER = {Jakub Jasi{\'n}ski},
DOI = {10.2307/2586586},
URL = {http://jdh.hamkins.org/superdestructibility/},
eprint = {1607.00684},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• Destruction or preservation as you like it
• J. D. Hamkins, “Destruction or preservation as you like it,” Annals of Pure and Applied Logic, vol. 91, iss. 2-3, pp. 191-229, 1998.
@article {Hamkins98:AsYouLikeIt,
AUTHOR = {Hamkins, Joel David},
TITLE = {Destruction or preservation as you like it},
JOURNAL = {Annals of Pure and Applied Logic},
FJOURNAL = {Annals of Pure and Applied Logic},
VOLUME = {91},
YEAR = {1998},
NUMBER = {2-3},
PAGES = {191--229},
ISSN = {0168-0072},
CODEN = {APALD7},
MRCLASS = {03E55 (03E35)},
MRNUMBER = {1604770 (99f:03071)},
MRREVIEWER = {Joan Bagaria},
DOI = {10.1016/S0168-0072(97)00044-4},
URL = {http://jdh.hamkins.org/asyoulikeit/},
eprint = {1607.00683},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• Canonical seeds and Prikry trees
• J. D. Hamkins, “Canonical seeds and Prikry trees,” Journal of Symbolic Logic, vol. 62, iss. 2, pp. 373-396, 1997.
@article {Hamkins97:Seeds,
AUTHOR = {Hamkins, Joel David},
TITLE = {Canonical seeds and {P}rikry trees},
JOURNAL = {Journal of Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {62},
YEAR = {1997},
NUMBER = {2},
PAGES = {373--396},
ISSN = {0022-4812},
CODEN = {JSYLA6},
MRCLASS = {03E40 (03E05 03E55)},
MRNUMBER = {1464105 (98i:03070)},
MRREVIEWER = {Douglas R.~Burke},
DOI = {10.2307/2275538},
URL = {http://jdh.hamkins.org/seeds},
}

• Fragile measurability
• J. Hamkins, “Fragile measurability,” Journal of Symbolic Logic, vol. 59, iss. 1, pp. 262-282, 1994.
@article {Hamkins94:FragileMeasurability,
AUTHOR = {Hamkins, Joel},
TITLE = {Fragile measurability},
JOURNAL = {Journal of Symbolic Logic},
VOLUME = {59},
YEAR = {1994},
NUMBER = {1},
PAGES = {262--282},
ISSN = {0022-4812},
CODEN = {JSYLA6},
MRCLASS = {03E35 (03E55)},
MRNUMBER = {1264978 (95c:03129)},
MRREVIEWER = {J.~M.~Henle},
DOI = {10.2307/2275264},
URL = {http://jdh.hamkins.org/fragilemeasurability/},
}

• Lifting and extending measures; fragile measurability
• J. D. Hamkins, “Lifting and extending measures; fragile measurability,” PhD Thesis, University of California, Berkeley, Department of Mathematics, 1994.
@PHDTHESIS{Hamkins94:Dissertation,
author = {Joel David Hamkins},
title = {Lifting and extending measures; fragile measurability},
school = {University of California, Berkeley},
institution = {University of California, Berkeley},
year = {1994},
month = {May},
note = {},
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annote = {},
url = {http://jdh.hamkins.org/dissertation/},
}

• A class of strong diamond principles
• J. D. Hamkins, “A class of strong diamond principles,” ArXiv e-prints, 2002.
@ARTICLE{Hamkins:LaverDiamond,
author = {Joel David Hamkins},
title = {A class of strong diamond principles},
journal = {ArXiv e-prints},
year = {2002},
eprint = {math/0211419},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://wp.me/p5M0LV-C},
}