- 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.” (manuscript 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 = {}, year = {}, volume = {}, number = {}, pages = {}, month = {}, note = {manuscript under review}, abstract = {}, keywords = {}, source = {}, eprint = {1606.03778}, archivePrefix = {arXiv}, primaryClass = {math.LO}, url = {http://jdh.hamkins.org/vopenka-principle-vopenka-scheme}, }`

- J. D. Hamkins, “The Vopěnka principle is inequivalent to but conservative over the Vopěnka scheme.” (manuscript under review)
- 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. " }`

- 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.
- Strongly uplifting cardinals and the boldface resurrection axioms
- J. D. Hamkins and T. Johnstone, “Strongly uplifting cardinals and the boldface resurrection axioms.” (under review, http://arxiv.org/abs/1403.2788)
`@ARTICLE{HamkinsJohnstone:StronglyUpliftingCardinalsAndBoldfaceResurrection, author = {Joel David Hamkins and Thomas Johnstone}, title = {Strongly uplifting cardinals and the boldface resurrection axioms}, journal = {}, year = {}, volume = {}, number = {}, pages = {}, month = {}, note = {under review, http://arxiv.org/abs/1403.2788}, eprint = {1403.2788}, archivePrefix = {arXiv}, primaryClass = {math.LO}, url = {http://jdh.hamkins.org/strongly-uplifting-cardinals-and-boldface-resurrection}, abstract = {}, keywords = {}, source = {}, }`

- J. D. Hamkins and T. Johnstone, “Strongly uplifting cardinals and the boldface resurrection axioms.” (under review, http://arxiv.org/abs/1403.2788)
- 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 Berlin Heidelberg}, 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 }`

- 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.
- 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,” to appear in Archive for Mathematical Logic (special issue in honor of Richard Laver).
`@ARTICLE{BagariaHamkinsTsaprounisUsuba:SuperstrongAndOtherLargeCardinalsAreNeverLaverIndestructible, author = {Joan Bagaria and Joel David Hamkins and Konstantinos Tsaprounis and Toshimichi Usuba}, title = {Superstrong and other large cardinals are never {Laver} indestructible}, journal = {to appear in Archive for Mathematical Logic (special issue in honor of Richard Laver)}, year = {}, volume = {}, number = {}, pages = {}, month = {}, note = {}, abstract = {}, keywords = {}, eprint = {1307.3486}, archivePrefix = {arXiv}, primaryClass = {math.LO}, url = {http://jdh.hamkins.org/superstrong-never-indestructible/}, comment = {http://jdh.hamkins.org/superstrong-never-indestructible/}, source = {}, }`

- J. Bagaria, J. D. Hamkins, K. Tsaprounis, and T. Usuba, “Superstrong and other large cardinals are never Laver indestructible,” to appear in Archive for Mathematical Logic (special issue in honor of Richard Laver).
- 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 Berlin Heidelberg}, 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}, }`

- 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.
- 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 = {Lect. Notes Ser. Inst. Math. Sci. 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://jdh.hamkins.org/multiverse-perspective-on-constructibility/}, eprint = {1210.6541}, archivePrefix = {arXiv}, primaryClass = {math.LO}, }`

- 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.
- 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 L\"owe}, title = {Moving up and down in the generic multiverse}, journal = {Logic and its Applications, ICLA 2013 LNCS}, publisher= {Springer Berlin Heidelberg}, 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://jdh.hamkins.org/up-and-down-in-the-generic-multiverse}, url = {http://arxiv.org/abs/1208.5061}, eprint = {1208.5061}, archivePrefix = {arXiv}, primaryClass = {math.LO}, abstract = {}, keywords = {}, source = {}, }`

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

- J. D. Hamkins and D. Seabold, “Well-founded Boolean ultrapowers as large cardinal embeddings,” , pp. 1-40. (preprint http://jdh.hamkins.org/boolean-ultrapowers/)
- Singular cardinals and strong extenders
- A. W. Apter, J. Cummings, and J. D. Hamkins, “Singular cardinals and strong extenders,” Cent. Eur. J. Math., 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 = {Cent. Eur. J. Math.}, FJOURNAL = {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}, }`

- A. W. Apter, J. Cummings, and J. D. Hamkins, “Singular cardinals and strong extenders,” Cent. Eur. J. Math., vol. 11, iss. 9, pp. 1628-1634, 2013.
- Inner models with large cardinal features usually obtained by forcing
- A. Apter, V. Gitman, and J. D. Hamkins, “Inner models with large cardinal features usually obtained by forcing,” Archive for Mathematical Logic, vol. 51, pp. 257-283, 2012. (10.1007/s00153-011-0264-5)
`@article {ApterGitmanHamkins2012:InnerModelsWithLargeCardinals, author = {Apter, Arthur and Gitman, Victoria and Hamkins, Joel David}, 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 Mathematical Logic}, publisher = {Springer Berlin / Heidelberg}, issn = {0933-5846}, keyword = {Mathematics and Statistics}, pages = {257--283}, volume = {51}, issue = {3}, url = {http://jdh.hamkins.org/innermodelswithlargecardinals/}, eprint = {1111.0856}, archivePrefix = {arXiv}, primaryClass = {math.LO}, doi = {10.1007/s00153-011-0264-5}, note = {10.1007/s00153-011-0264-5}, year = {2012} }`

- A. Apter, V. Gitman, and J. D. Hamkins, “Inner models with large cardinal features usually obtained by forcing,” Archive for Mathematical Logic, vol. 51, pp. 257-283, 2012. (10.1007/s00153-011-0264-5)
- What is the theory ZFC without power set?
- V. Gitman, J. D. Hamkins, and T. A.~Johnstone, “What is the theory ZFC without Powerset?,” Mathematical Logic Quarterly, vol. 62, iss. 4–5, pp. 391-406, 2016.
`@ARTICLE{GitmanHamkinsJohnstone:WhatIsTheTheoryZFC-Powerset?, AUTHOR = {Victoria Gitman and Joel David Hamkins and Thomas A.~Johnstone}, TITLE = {What is the theory {ZFC} without {Powerset}?}, JOURNAL = {Mathematical Logic Quarterly}, 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://arxiv.org/abs/1110.2430}, source = {}, }`

- V. Gitman, J. D. Hamkins, and T. A.~Johnstone, “What is the theory ZFC without Powerset?,” Mathematical Logic Quarterly, vol. 62, iss. 4–5, pp. 391-406, 2016.
- 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://www.sciencedirect.com/science/article/pii/S0168007212000966", author = "Joel David Hamkins and Greg Kirmayer and Norman Lewis Perlmutter" }`

- 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.
- Indestructible strong unfoldability
- J. D. Hamkins and T. A. Johnstone, “Indestructible strong unfoldability,” Notre Dame J.~Form.~Log., 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 J.~Form.~Log.}, 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.~K{\"o}nig}, DOI = {10.1215/00294527-2010-018}, URL = {http://dx.doi.org/10.1215/00294527-2010-018}, file = F }`

- J. D. Hamkins and T. A. Johnstone, “Indestructible strong unfoldability,” Notre Dame J.~Form.~Log., vol. 51, iss. 3, pp. 291-321, 2010.
- Tall cardinals
- J. D. Hamkins, “Tall cardinals,” MLQ Math.~Log.~Q., vol. 55, iss. 1, pp. 68-86, 2009.
`@ARTICLE{Hamkins2009:TallCardinals, AUTHOR = {Hamkins, Joel D.}, TITLE = {Tall cardinals}, JOURNAL = {MLQ Math.~Log.~Q.}, FJOURNAL = {MLQ.~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://dx.doi.org/10.1002/malq.200710084}, file = F }`

- J. D. Hamkins, “Tall cardinals,” MLQ Math.~Log.~Q., vol. 55, iss. 1, pp. 68-86, 2009.
- 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://dx.doi.org/10.1090/S0002-9939-08-09727-X}, file = F }`

- 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.
- Large cardinals with few measures
- J. Apter Arthur W.~and 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 = {Apter, Arthur W.~and Cummings, James and Hamkins, Joel David}, 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://dx.doi.org/10.1090/S0002-9939-07-08786-2}, eprint = {math/0603260}, archivePrefix = {arXiv}, primaryClass = {math.LO}, file = F }`

- J. Apter Arthur W.~and Cummings and J. D. Hamkins, “Large cardinals with few measures,” Proc.~Amer.~Math.~Soc., vol. 135, iss. 7, pp. 2291-2300, 2007.
- 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://dx.doi.org/10.4064/fm180-3-4}, eprint = {math/0307229}, archivePrefix = {arXiv}, primaryClass = {math.LO}, file = F, }`

- 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.
- Exactly controlling the non-supercompact strongly compact cardinals
- J. D. Apter Arthur W.~and Hamkins, “Exactly controlling the non-supercompact strongly compact cardinals,” J.~Symbolic Logic, vol. 68, iss. 2, pp. 669-688, 2003.
`@ARTICLE{ApterHamkins2003:ExactlyControlling, AUTHOR = {Apter, Arthur W.~and Hamkins, Joel David}, TITLE = {Exactly controlling the non-supercompact strongly compact cardinals}, JOURNAL = {J.~Symbolic Logic}, FJOURNAL = {The 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}, URL = {http://projecteuclid.org/getRecord?id=euclid.jsl/1052669070}, eprint = {math/0301016}, archivePrefix = {arXiv}, primaryClass = {math.LO}, }`

- J. D. Apter Arthur W.~and Hamkins, “Exactly controlling the non-supercompact strongly compact cardinals,” J.~Symbolic Logic, vol. 68, iss. 2, pp. 669-688, 2003.
- A simple maximality principle
- J. D. Hamkins, “A simple maximality principle,” J.~Symbolic Logic, vol. 68, iss. 2, pp. 527-550, 2003.
`@article{Hamkins2003:MaximalityPrinciple, AUTHOR = {Hamkins, Joel David}, TITLE = {A simple maximality principle}, JOURNAL = {J.~Symbolic Logic}, FJOURNAL = {The 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://projecteuclid.org/getRecord?id=euclid.jsl/1052669062}, month = {June}, eprint = {math/0009240}, archivePrefix = {arXiv}, primaryClass = {math.LO}, }`

- J. D. Hamkins, “A simple maximality principle,” J.~Symbolic Logic, vol. 68, iss. 2, pp. 527-550, 2003.
- Indestructibility and the level-by-level agreement between strong compactness and supercompactness
- J. D. Apter Arthur W.~and Hamkins, “Indestructibility and the level-by-level agreement between strong compactness and supercompactness,” J.~Symbolic Logic, vol. 67, iss. 2, pp. 820-840, 2002.
`@ARTICLE{ApterHamkins2002:LevelByLevel, AUTHOR = {Apter, Arthur W.~and Hamkins, Joel David}, TITLE = {Indestructibility and the level-by-level agreement between strong compactness and supercompactness}, JOURNAL = {J.~Symbolic Logic}, FJOURNAL = {The 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://dx.doi.org/10.2178/jsl/1190150111}, eprint = {math/0102086}, archivePrefix = {arXiv}, primaryClass = {math.LO}, }`

- J. D. Apter Arthur W.~and Hamkins, “Indestructibility and the level-by-level agreement between strong compactness and supercompactness,” J.~Symbolic Logic, vol. 67, iss. 2, pp. 820-840, 2002.
- Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata
- J. D. Apter Arthur W.~and Hamkins, “Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata,” MLQ Math.~Log.~Q., vol. 47, iss. 4, pp. 563-571, 2001.
`@ARTICLE{ApterHamkins2001:IndestructibleWC, AUTHOR = {Apter, Arthur W.~and Hamkins, Joel David}, TITLE = {Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata}, JOURNAL = {MLQ Math.~Log.~Q.}, FJOURNAL = {MLQ.~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://dx.doi.org/10.1002/1521-3870(200111)47:4<563::AID-MALQ563>3.0.CO;2-#}, eprint = {math/9907046}, archivePrefix = {arXiv}, primaryClass = {math.LO}, }`

- J. D. Apter Arthur W.~and Hamkins, “Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata,” MLQ Math.~Log.~Q., vol. 47, iss. 4, pp. 563-571, 2001.
- 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://dx.doi.org/10.1007/s001530050169}, eprint = {math/9902079}, archivePrefix = {arXiv}, primaryClass = {math.LO}, }`

- J. D. Hamkins, “The wholeness axioms and $V=\rm HOD$,” Arch.~Math.~Logic, vol. 40, iss. 1, pp. 1-8, 2001.
- 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://dx.doi.org/10.1016/S0168-0072(99)00010-X}, eprint = {math/9808012}, archivePrefix = {arXiv}, primaryClass = {math.LO}, }`

- J. D. Hamkins, “The lottery preparation,” Ann.~Pure Appl.~Logic, vol. 101, iss. 2-3, pp. 103-146, 2000.
- 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 = "", doi = "10.1023/A:1017327516639", url = "http://dx.doi.org/10.1023/A:1017327516639", issn = "0039-3215", keywords = "", source = "", file = F }`

- J. D. Hamkins, “book review of The Higher Infinite, Akihiro Kanamori,” Studia Logica, vol. 65, iss. 3, pp. 443-446, 2000.
- Gap forcing: generalizing the Lévy-Solovay theorem
- J. D. Hamkins, “Gap forcing: generalizing the Lévy-Solovay theorem,” Bull.~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 = {Bull.~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://dx.doi.org/10.2307/421092}, month = {June}, eprint = {math/9901108}, archivePrefix = {arXiv}, primaryClass = {math.LO}, }`

- J. D. Hamkins, “Gap forcing: generalizing the Lévy-Solovay theorem,” Bull.~Symbolic Logic, vol. 5, iss. 2, pp. 264-272, 1999.
- Universal indestructibility
- J. D. Apter Arthur W.~and Hamkins, “Universal indestructibility,” Kobe J.~Math., vol. 16, iss. 2, pp. 119-130, 1999.
`@article {ApterHamkins99:UniversalIndestructibility, AUTHOR = {Apter, Arthur W.~and Hamkins, Joel David}, TITLE = {Universal indestructibility}, JOURNAL = {Kobe J.~Math.}, FJOURNAL = {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}, }`

- J. D. Apter Arthur W.~and Hamkins, “Universal indestructibility,” Kobe J.~Math., vol. 16, iss. 2, pp. 119-130, 1999.
- Superdestructibility: a dual to Laver's indestructibility
- J. D. Hamkins and S. Shelah, “Superdestructibility: a dual to Laver’s indestructibility,” J.~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 = {J.~Symbolic Logic}, FJOURNAL = {The Journal of Symbolic Logic}, VOLUME = {63}, YEAR = {1998}, NUMBER = {2}, PAGES = {549--554}, ISSN = {0022-4812}, CODEN = {JSYLA6}, MRCLASS = {03E55 (03E40)}, MRNUMBER = {1625927 (99m:03106)}, MRREVIEWER = {Douglas R.~Burke}, DOI = {10.2307/2586848}, URL = {http://dx.doi.org/10.2307/2586848}, note = {[HmSh:618]}, eprint = {math/9612227}, archivePrefix = {arXiv}, primaryClass = {math.LO}, }`

- J. D. Hamkins and S. Shelah, “Superdestructibility: a dual to Laver’s indestructibility,” J.~Symbolic Logic, vol. 63, iss. 2, pp. 549-554, 1998. ([HmSh:618])
- Small forcing makes any cardinal superdestructible
- J. D. Hamkins, “Small forcing makes any cardinal superdestructible,” J.~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 = {J.~Symbolic Logic}, FJOURNAL = {The 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}, }`

- J. D. Hamkins, “Small forcing makes any cardinal superdestructible,” J.~Symbolic Logic, vol. 63, iss. 1, pp. 51-58, 1998.
- Destruction or preservation as you like it
- J. D. Hamkins, “Destruction or preservation as you like it,” Ann.~Pure Appl.~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 = {Ann.~Pure Appl.~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}, }`

- J. D. Hamkins, “Destruction or preservation as you like it,” Ann.~Pure Appl.~Logic, vol. 91, iss. 2-3, pp. 191-229, 1998.
- Canonical seeds and Prikry trees
- J. D. Hamkins, “Canonical seeds and Prikry trees,” J.~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 = {J.~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://dx.doi.org/10.2307/2275538}, }`

- J. D. Hamkins, “Canonical seeds and Prikry trees,” J.~Symbolic Logic, vol. 62, iss. 2, pp. 373-396, 1997.
- Fragile measurability
- J. Hamkins, “Fragile measurability,” J.~Symbolic Logic, vol. 59, iss. 1, pp. 262-282, 1994.
`@article {Hamkins94:FragileMeasurability, AUTHOR = {Hamkins, Joel}, TITLE = {Fragile measurability}, JOURNAL = {J.~Symbolic Logic}, FJOURNAL = {The 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://dx.doi.org/10.2307/2275264}, }`

- J. Hamkins, “Fragile measurability,” J.~Symbolic Logic, vol. 59, iss. 1, pp. 262-282, 1994.
- 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}, address = {Department of Mathematics}, month = {May}, note = {}, key = {}, annote = {}, }`

- J. D. Hamkins, “Lifting and extending measures; fragile measurability,” PhD Thesis, University of California, Berkeley, Department of Mathematics, 1994.
- A class of strong diamond principles
- J. D. Hamkins, “A class of strong diamond principles,” mathematics arxiv preprint http://arxiv.org/abs/math/0211419, 2002.
`@ARTICLE{Hamkins:LaverDiamond, author = {Joel David Hamkins}, title = {A class of strong diamond principles}, journal = {mathematics arxiv preprint http://arxiv.org/abs/math/0211419}, year = {2002}, eprint = {math/0211419}, archivePrefix = {arXiv}, primaryClass = {math.LO}, }`

- J. D. Hamkins, “A class of strong diamond principles,” mathematics arxiv preprint http://arxiv.org/abs/math/0211419, 2002.