Joel David Hamkins

Ali Enayat and Joel David Hamkins. “ZFC proves that the class of ordinals is not weakly compact for definable classes”. J. Symbolic Logic 83.1 (2018), pp. 146–164. doi:10.1017/jsl.2017.75. arXiv:1610.02729. (http://jdh.hamkins.org/ord-is-not-definably-weakly-compact)

Gunter Fuchs, Victoria Gitman, and Joel David Hamkins. “Ehrenfeucht’s Lemma in Set Theory”. Notre Dame J. Formal Logic 59.3 (2018), pp. 355–370. doi:10.1215/00294527-2018-0007. arXiv:1501.01918. (http://jdh.hamkins.org/ehrenfeuchts-lemma-in-set-theory)

Victoria Gitman and Joel David Hamkins. “A model of the generic Vopӗnka principle in which the ordinals are not Mahlo”. Archive for Mathematical Logic (May 2018), pp. 1–21. issn:0933-5846. doi:10.1007/s00153-018-0632-5. arXiv:1706.00843. (http://wp.me/p5M0LV-1xT)

C. D. A. Evans, Joel David Hamkins, and Norman Lewis Perlmutter. “A position in infinite chess with game value ω4”. Integers 17 (2017), Paper No. G4, 22. arXiv:1510.08155. (http://wp.me/p5M0LV-1c5)

Gunter Fuchs, Victoria Gitman, and Joel David Hamkins. “Incomparable ω1-like models of set theory”. Math. Logic Q. (2017), pp. 1–11. issn:1521-3870. doi:10.1002/malq.201500002. arXiv:1501.01022. (http://jdh.hamkins.org/incomparable-omega-one-like-models-of-set-theory)

Michal Tomasz Godziszewski and Joel David Hamkins. “Computable Quotient Presentations of Models of Arithmetic and Set Theory”. In: Logic, Language, Information, and Computation: 24th International Workshop, WoLLIC 2017, London, UK, July 18-21, 2017, Proceedings. Ed. by Juliette Kennedy and Ruy J.G.B. de Queiroz. Springer, 2017, pp. 140–152. isbn:978-3-662-55386-2. doi:10.1007/978-3-662-55386-2 10. arXiv:1702.08350. (http://wp.me/p5M0LV-1tW)

Joel David Hamkins and Thomas Johnstone. “Strongly uplifting cardinals and the boldface resurrection axioms”. Archive for Mathematical Logic 56.7 (2017), pp. 1115–1133. issn:1432-0665. doi:10.1007/s00153-017-0542-y. arXiv:1403.2788. (http://wp.me/p5M0LV-IE)

Joan Bagaria, Joel David Hamkins, Konstantinos Tsaprounis, and Toshimichi Usuba. “Superstrong and other large cardinals are never Laver indestructible”. Arch. Math. Logic 55.1-2 (2016). special volume in memory of R. Laver, pp. 19–35. issn:0933-5846. doi:10.1007/s00153-015-0458-3. arXiv:1307.3486. (http://jdh.hamkins.org/superstrong-never-indestructible)

Victoria Gitman and Joel David Hamkins. “Open determinacy for class games”. In: Foundations of Mathematics, Logic at Harvard, Essays in Honor of Hugh Woodin’s 60th Birthday. Ed. by Andrés E. Caicedo, James Cummings, Peter Koellner, and Paul Larson. AMS Contemporary Mathematics. Newton Institute preprint ni15064. 2016. arXiv:1509.01099. (http://wp.me/p5M0LV-1af)

Victoria Gitman, Joel David Hamkins, and Thomas A. Johnstone. “What is the theory ZFC without Powerset?” Math. Logic Q. 62.4–5 (2016), pp. 391–406. issn:0942-5616. doi:10.1002/malq.201500019. arXiv:1110.2430. (http://jdh.hamkins.org/what-is-the-theory-zfc-without-power-set)

Joel David Hamkins. “Upward closure and amalgamation in the generic multiverse of a countable model of set theory”. RIMS Kyôkyûroku (2016), pp. 17–31. issn:1880-2818. arXiv:1511.01074. (http://wp.me/p5M0LV-1cv)

Joel David Hamkins and Makoto Kikuchi. “Set-theoretic mereology”. Logic and Logical Philosophy, special issue “Mereology and beyond, part II” 25.3 (2016). Ed. by A. C. Varzi and R. Gruszczy´ nski, pp. 285–308. issn:1425-3305. doi:10.12775/LLP.2016.007. arXiv:1601.06593. (http://jdh.hamkins.org/set-theoretic-mereology)

Joel David Hamkins and Cole Leahy. “Algebraicity and Implicit Definability in Set Theory”. Notre Dame J. Formal Logic 57.3 (2016), pp. 431–439. issn:0029-4527. doi:10.1215/00294527-3542326. arXiv:1305.5953. (http://jdh.hamkins.org/algebraicity-and-implicit-definability)

Yong Cheng, Sy-David Friedman, and Joel David Hamkins. “Large cardinals need not be large in HOD”. Annals of Pure and Applied Logic 166.11 (2015), pp. 1186 –1198. issn:0168-0072. doi:10.1016/j.apal.2015.07.004. arXiv:1407.6335. (http://jdh.hamkins.org/large-cardinals-need-not-be-large-in-hod)

Brent Cody, Moti Gitik, Joel David Hamkins, and Jason A. Schanker. “The least weakly compact cardinal can be unfoldable, weakly measurable and nearly θ supercompact”. Archive for Mathematical Logic (2015), pp. 1–20. issn:0933-5846. doi:10.1007/s00153-015-0423-1. arXiv:1305.5961. (http://jdh.hamkins.org/least-weakly-compact)

Gunter Fuchs, Joel David Hamkins, and Jonas Reitz. “Set-theoretic geology”. Annals of Pure and Applied Logic 166.4 (2015), pp. 464–501. issn:0168-0072. doi:10.1016/j.apal.2014.11.004. arXiv:1107.4776. (http://jdh.hamkins.org/set-theoreticgeology)

Joel David Hamkins. “Is the dream solution of the continuum hypothesis attainable?” Notre Dame J. Formal Logic 56.1 (2015), pp. 135–145. issn:0029-4527. doi:10.1215/00294527-2835047. arXiv:1203.4026. (http://jdh.hamkins.org/dream-solution-of-ch)

Joel David Hamkins, George Leibman, and Benedikt Löwe. “Structural connections between a forcing class and its modal logic”. Israel J. Math. 207.2 (2015), pp. 617–651. issn:0021-2172. doi:10.1007/s11856-015-1185-5. arXiv:1207.5841. (http://wp.me/p5M0LV-kf)

Ali Sadegh Daghighi, Mohammad Golshani, Joel David Hamkins, and Emil Jeřábek. “The foundation axiom and elementary self-embeddings of the universe”. In: Infinity, computability, and metamathematics: Festschrift celebrating the 60th birthdays of Peter Koepke and Philip Welch. Ed. by S. Geschke, B. Löwe, and P. Schlicht. Vol. 23. Tributes. Coll. Publ., London, 2014, pp. 89–112. arXiv:1311.0814. (http://jdh.hamkins.org/the-role-of-foundation-in-the-kunen-inconsistency)

C. D. A. Evans and Joel David Hamkins. “Transfinite game values in infinite chess”. Integers 14 (2014), Paper No. G2, 36. issn:1553-1732. arXiv:1302.4377. (http://jdh.hamkins.org/game-values-in-infinite-chess)

Joel David Hamkins. “A multiverse perspective on the axiom of constructibility”. In: Infinity and Truth. Vol. 25. LNS Math Natl. Univ. Singap. World Sci. Publ., Hackensack, NJ, 2014, pp. 25–45. doi:10.1142/9789814571043 0002. arXiv:1210.6541. (http://wp.me/p5M0LV-qE)

Joel David Hamkins and Thomas Johnstone. “Resurrection axioms and uplifting cardinals”. Archive for Mathematical Logic 53.3-4 (2014), p. 463–485. issn:0933-5846. doi:10.1007/s00153-014-0374-y. arXiv:1307.3602. (http://jdh.hamkins.org/resurrection-axioms-and-uplifting-cardinals)

Arthur W. Apter, James Cummings, and Joel David Hamkins. “Singular cardinals and strong extenders”. Central European J. Math. 11.9 (2013), pp. 1628–1634. issn:1895-1074. doi:10.2478/s11533-013-0265-1. arXiv:1206.3703. (http://jdh.hamkins.org/singular-cardinals-strong-extenders)

Samuel Coskey and Joel David Hamkins. “Infinite time Turing machines and an application to the hierarchy of equivalence relations on the reals”. In: Effective mathematics of the uncountable. Vol. 41. Lect. Notes Log. Assoc. Symbol. Logic, La Jolla, CA, 2013, pp. 33–49. arXiv:1101.1864. (http://jdh.hamkins.org/ittms-and-applications)

Joel David Hamkins. “Every countable model of set theory embeds into its own constructible universe”. J. Math. Logic 13.2 (2013), pp. 1350006, 27. issn:0219-0613. doi:10.1142/S0219061313500062. arXiv:1207.0963. (http://wp.me/p5M0LV-jn) 

Joel David Hamkins, David Linetsky, and Jonas Reitz. “Pointwise definable models of set theory”. J. Symbolic Logic 78.1 (2013), pp. 139–156. issn:0022-4812. doi:10.2178/jsl.7801090. arXiv:1105.4597. (http://jdh.hamkins.org/pointwisedefinablemodelsofsettheory)

Joel David Hamkins and Benedikt Löwe. “Moving up and down in the generic multiverse”. Logic and its Applications, ICLA 2013 LNCS 7750 (2013). Ed. by Kamal Lodaya, pp. 139–147. doi:10.1007/978-3-642-36039-8 13. arXiv:1208.5061. (http://wp.me/p5M0LV-od)

Arthur W. Apter, Victoria Gitman, and Joel David Hamkins. “Inner models with large cardinal features usually obtained by forcing”. Archive for Math. Logic 51 (3 2012), pp. 257–283. issn:0933-5846. doi:10.1007/s00153-011-0264-5. arXiv:1111.0856. (http://jdh.hamkins.org/innermodels)

Dan Brumleve, Joel David Hamkins, and Philipp Schlicht. “The Mate-in-n Problem of Infinite Chess Is Decidable”. In: How the World Computes. Ed. by S. Barry Cooper, Anuj Dawar, and Benedikt Löwe. Vol. 7318. Lecture Notes in Computer Science. Springer, 2012, pp. 78–88. isbn: 978-3-642-30869-7. doi:10.1007/978-3-642-30870-3 9. arXiv:1201.5597. (http://wp.me/p5M0LV-f8)

Samuel Coskey, Joel David Hamkins, and Russell Miller. “The hierarchy of equivalence relations on the natural numbers under computable reducibility”. Computability 1.1 (2012), pp. 15–38. doi:10.3233/COM-2012-004. arXiv:1109.3375. (http://jdh.hamkins.org/equivalence-relations-on-naturals)

Joel David Hamkins. “The set-theoretic multiverse”. Review of Symbolic Logic 5 (2012), pp. 416–449. doi:10.1017/S1755020311000359. arXiv:1108.4223. (http://jdh.hamkins.org/themultiverse)

Joel David Hamkins, Greg Kirmayer, and Norman Lewis Perlmutter. “Generalizations of the Kunen inconsistency”. Annals of Pure and Applied Logic 163.12 (2012), pp. 1872 –1890. issn:0168-0072. doi:10.1016/j.apal.2012.06.001. arXiv:1106.1951. (http://jdh.hamkins.org/generalizationsofkuneninconsistency)

Joel David Hamkins and Justin Palumbo. “The rigid relation principle, a new weak choice principle”. Math. Logic Q. 58.6 (2012), pp. 394–398. issn:0942-5616. doi:10.1002/malq.201100081. arXiv:1106.4635. (http://jdh.hamkins.org/therigidrelationprincipleanewweakacprinciple)

Samuel Coskey and Joel David Hamkins. “Infinite time decidable equivalence relation theory”. Notre Dame J. Formal Logic 52.2 (2011), pp. 203–228. issn:0029-4527. doi:10.1215/00294527-1306199. arXiv:0910.4616. (http://wp.me/p5M0LV-3M)

Joel David Hamkins. “Pointwise definable models of set theory, extended abstract”. Mathematisches Forschungsinstitut Oberwolfach Report 8.1, 02/2011 (2011), pp. 128–131. doi:10.4171/OWR/2011/02. (http://wp.me/p5M0LV-4n)

Joel David Hamkins. “The Set-theoretic Multiverse : A Natural Context for Set Theory”. Annals of the Japan Association for Philosophy of Science 19 (2011), pp. 37–55. issn:0453-0691. doi:10.4288/jafpos.19.0 37. (http://jdh.hamkins.org/themultiverseanaturalcontext)

Victoria Gitman and Joel David Hamkins. “A natural model of the multiverse axioms”. Notre Dame J. Formal Logic 51.4 (2010), pp. 475–484. issn:0029-4527. doi:10.1215/00294527-2010-030. arXiv:1104.4450. (http://wp.me/p5M0LV-3I)

Joel David Hamkins and Thomas A. Johnstone. “Indestructible strong unfoldability”. Notre Dame J. Formal Logic 51.3 (2010), pp. 291–321. issn:0029-4527. doi:10.1215/00294527-2010-018. (http://jdh.hamkins.org/indestructiblestrongunfoldability)

Gunter Fuchs and Joel David Hamkins. “Degrees of rigidity for Souslin trees”. J. Symbolic Logic 74.2 (2009), pp. 423–454. issn:0022-4812. doi:10.2178/jsl/1243948321. arXiv:math/0602482. (http://wp.me/p5M0LV-3A)

Joel D. Hamkins. “Tall cardinals”. Math. Logic Q. 55.1 (2009), pp. 68–86. issn:0942-5616. doi:10.1002/malq.200710084. (http://wp.me/p5M0LV-3y)

Joel David Hamkins. “Some second order set theory”. In: Logic and its applications. Ed. By R. Ramanujam and S. Sarukkai. Vol. 5378. Lecture Notes in Comput. Sci. Springer, 2009, pp. 36–50. doi:10.1007/978-3-540-92701-3 3. (http://wp.me/p5M0LV-3E)

Joel David Hamkins and Thomas A. Johnstone. “The proper and semi-proper forcing axioms for forcing notions that preserve ℵ2 or ℵ3”. Proc. Amer. Math. Soc. 137.5 (2009), pp. 1823–1833. issn:0002-9939. doi:10.1090/S0002-9939-08-09727-X. (http://wp.me/p5M0LV-3v)

Joel David Hamkins and Russell G. Miller. “Post’s problem for ordinal register machines: an explicit approach”. Ann. Pure Appl. Logic 160.3 (2009), pp. 302–309. issn:0168-0072. doi:10.1016/j.apal.2009.01.004. (http://wp.me/p5M0LV-3C)

Gunter Fuchs and Joel David Hamkins. “Changing the heights of automorphism towers by forcing with Souslin trees over L”. J. Symbolic Logic 73.2 (2008), pp. 614–633. issn:0022-4812. doi:10.2178/jsl/1208359063. arXiv:math/0702768. (http://wp.me/p5M0LV-3l)

Joel David Hamkins and Benedikt Löwe. “The modal logic of forcing”. Trans. AMS 360.4 (2008), pp. 1793–1817. issn:0002-9947. doi:10.1090/S0002-9947-07-04297-3. arXiv:math/0509616.(http://wp.me/p5M0LV-3h)

Joel David Hamkins, Russell Miller, Daniel Seabold, and Steve Warner. “Infinite time computable model theory”. In: New Computational Paradigms: Changing Conceptions of What is Computable. Ed. by S. B. Cooper, Benedikt Löwe, and Andrea Sorbi. New York: Springer, 2008, pp. 521–557. isbn: 0-387-36033-6. (http://wp.me/p5M0LV-3t)

Joel David Hamkins, Jonas Reitz, and W. Hugh Woodin. “The ground axiom is consistent with V 6= HOD”. Proc. Amer. Math. Soc. 136.8 (2008), pp. 2943–2949. issn:0002-9939. doi:10.1090/S0002-9939-08-09285-X. (http://wp.me/p5M0LV-3j)

Arthur W. Apter, James Cummings, and Joel David Hamkins. “Large cardinals with few measures”. Proc. Amer. Math. Soc. 135.7 (2007), pp. 2291–2300. issn:0002-9939. doi:10.1090/S0002-9939-07-08786-2. arXiv:math/0603260. (http://jdh.hamkins.org/largecardinalswithfewmeasures)

Joel David Hamkins. “A Survey of Infinite Time Turing Machines”. In: Machines, Computations, and Universality - 5th International Conference MCU 2007. Ed. by Jérôme Durand-Lose and Maurice Margenstern. Vol. 4664. Lecture Notes in Computer Science. Orleans, France, 2007, pp. 62–71. doi:10.1007/978-3-540-74593-8 5. (http://wp.me/p5M0LV-3d)

Joel David Hamkins, David Linetsky, and Russell Miller. “The Complexity of Quickly Decidable ORM-Decidable Sets”. In: Computation and Logic in the Real World - CiE 2007. Ed. by B. Cooper, B. Löwe, and A. Sorbi. Vol. 4497. Proc. LNCS. Siena, Italy, 2007, pp. 488–496. doi:10.1007/978-3-540-73001-9 51. (http://wp.me/p5M0LV-3b)

Joel David Hamkins and Russell Miller. “Post’s Problem for Ordinal Register Machines”. In: Computation and Logic in the Real World—CiE 2007. Ed. by B. Cooper, B. Löwe, and A. Sorbi. Vol. 4497. Proc. LNCS. Siena, Italy, 2007, pp. 358–367. doi:10.1007/978-3-540-73001-9 37. (http://wp.me/p5M0LV-39)

Mirna Džamonja and Joel David Hamkins. “Diamond (on the regulars) can fail at any strongly unfoldable cardinal”. Ann. Pure Appl. Logic 144.1-3 (2006). Conference in honor of sixtieth birthday of James E. Baumgartner, pp. 83–95. issn:0168-0072. doi:10.1016/j.apal.2006.05.001. arXiv:math/0409304. (http://jdh.hamkins.org/diamondcanfail)

Joel David Hamkins and Alexei Miasnikov. “The halting problem is decidable on a set of asymptotic probability one”. Notre Dame J. Formal Logic 47.4 (2006), pp. 515–524. issn:0029-4527. doi:10.1305/ndjfl/1168352664. arXiv:math/0504351. (http://jdh.hamkins.org/haltingproblemdecidable)

Joel David Hamkins and Daniel Seabold. “Well-founded Boolean ultrapowers as large cardinal embeddings” (2006), pp. 1–40. arXiv:1206.6075. (http://jdh.hamkins.org/boolean-ultrapowers)

Vinay Deolalikar, Joel David Hamkins, and Ralf Schindler. “P ≠ NP ∩ co-NP for infinite time Turing machines”. J. Logic & Computation 15.5 (2005), pp. 577–592. issn:0955-792X. doi:10.1093/logcom/exi022. arXiv:math/0307388. (http://jdh.hamkins.org/np-conp)

Joel David Hamkins. “Infinitary computability with infinite time Turing machines”. In: New Computational Paradigms. Ed. by B. Cooper and B. Löwe. Vol. 3526. LNCS. CiE. Springer-Verlag, 2005. isbn: 3-540-26179-6. doi:10.1007/11494645 22. (http://wp.me/p5M0LV-2H)

Joel David Hamkins. “The Ground Axiom”. Mathematisches Forschungsinstitut Oberwolfach Report 55 (2005), pp. 3160–3162. arXiv:1607.00723. (http://jdh.hamkins.org/thegroundaxiom)

Joel David Hamkins and W. Hugh Woodin. “The necessary maximality principle for c.c.c. forcing is equiconsistent with a weakly compact cardinal”. Math. Logic Q. 51.5 (2005), pp. 493–498. issn:0942-5616. doi:10.1002/malq.200410045. arXiv:math/0403165. (http://wp.me/s5M0LV-nmpccc)

Joel David Hamkins. “Supertask computation”. In: Classical and new paradigms of computation and their complexity hierarchies. Vol. 23. Trends Log. Stud. Log. Libr. Papers of the conference “Foundations of the Formal Sciences III” held in Vienna, September 21-24, 2001. Dordrecht: Kluwer Acad. Publ., 2004, pp. 141–158. doi:10.1007/978-1-4020-2776-5 8. arXiv:math/0212049. (http://jdh.hamkins.org/supertaskcomputation)

Arthur W. Apter and Joel David Hamkins. “Exactly controlling the non-supercompact strongly compact cardinals”. J. Symbolic Logic 68.2 (2003), pp. 669–688. issn:0022-4812. doi:10.2178/jsl/1052669070. arXiv:math/0301016. (http://wp.me/p5M0LV-2x)

Joel David Hamkins. “A simple maximality principle”. J. Symbolic Logic 68.2 (2003), pp. 527–550. issn:0022-4812. doi:10.2178/jsl/1052669062. arXiv:math/0009240. (http://wp.me/p5M0LV-2v)

Joel David Hamkins. “Extensions with the approximation and cover properties have no new large cardinals”. Fund. Math. 180.3 (2003), pp. 257–277. issn:0016-2736. doi:10.4064/fm180-3-4. arXiv:math/0307229. (http://wp.me/p5M0LV-2B)

Joel David Hamkins and Philip D. Welch. “Pf ≠ NPf for almost all f”. Math. Logic Q. 49.5 (2003), pp. 536–540. issn:0942-5616. doi:10.1002/malq.200310057. arXiv:math/0212046.(http://jdh.hamkins.org/pf-npf)

Arthur W. Apter and Joel David Hamkins. “Indestructibility and the level-by-level agreement between strong compactness and supercompactness”. J. Symbolic Logic 67.2 (2002), pp. 820–840. issn:0022-4812. doi:10.2178/jsl/1190150111. arXiv:math/0102086. (http://wp.me/p5M0LV-2i)

Donniell Fishkind, Joel David Hamkins, and Barbara Montero. “New inconsistencies in infinite utilitarianism”. Australasian J. Philosophy 80.2 (2002), pp. 178–190. doi:10.1093/ajp/80.2.178. (http://jdh.hamkins.org/newinconsistencies)

Joel David Hamkins. “A class of strong diamond principles”. ArXiv e-prints (2002). arXiv:math/0211419. (http://wp.me/p5M0LV-C)

Joel David Hamkins. “How tall is the automorphism tower of a group?” In: Logic and algebra. Ed. by Yi Zhang. Vol. 302. Contemporary Math. Providence, RI: AMS, 2002, pp. 49–57. doi:10.1090/conm/302. (http://wp.me/s5M0LV-howtall)

Joel David Hamkins. “Infinite time Turing machines”. Minds and Machines 12.4 (2002). special issue devoted to hypercomputation, pp. 521–539. arXiv:math/0212047. (http://wp.me/p5M0LV-2e)

Joel David Hamkins and Andrew Lewis. “Post’s problem for supertasks has both positive and negative solutions”. Arch. Math. Logic 41.6 (2002), pp. 507–523. issn:0933-5846. doi:10.1007/s001530100112. arXiv:math/9808128. (http://jdh.hamkins.org/postproblem)

Arthur W. Apter and Joel David Hamkins. “Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata”. Math. Logic Q. 47.4 (2001), pp. 563–571. issn:0942-5616. doi:10.1002/1521-3870(200111)47:4%3C563::AID-MALQ563%3E3.0.CO;2-%23. arXiv:math/9907046. (http://jdh.hamkins.org/indestructiblewc)

Joel David Hamkins. “Gap forcing”. Israel J. Math. 125 (2001), pp. 237–252. issn:0021-2172. doi:10.1007/BF02773382. arXiv:math/9808011. (http://jdh.hamkins.org/gapforcing)

Joel David Hamkins. “The wholeness axioms and V = HOD”. Arch. Math. Logic 40.1 (2001), pp. 1–8. issn:0933-5846. doi:10.1007/s001530050169. arXiv:math/9902079. (http://wp.me/p5M0LV-1k)

Joel David Hamkins. “Unfoldable cardinals and the GCH”. J. Symbolic Logic 66.3 (2001), pp. 1186–1198. issn:0022-4812. doi:10.2307/2695100. arXiv:math/9909029. (http://wp.me/p5M0LV-28)

Joel David Hamkins and Daniel Evan Seabold. “Infinite Time Turing Machines With Only One Tape”. Math. Logic Q. 47.2 (2001), pp. 271–287. issn:1521-3870. doi:10.1002/1521-3870(200105)47:2h271::AID-MALQ271i3.0.CO;2-6. arXiv:math/9907044. (http://jdh.hamkins.org/onetape)

Joel David Hamkins. “The lottery preparation”. Ann. Pure Appl. Logic 101.2-3 (2000), pp. 103–146. issn:0168-0072. doi:10.1016/S0168-0072(99)00010-X. arXiv:math/9808012. (http://jdh.hamkins.org/lotterypreparation)

Joel David Hamkins and Andy Lewis. “Infinite time Turing machines”. J. Symbolic Logic 65.2 (2000), pp. 567–604. issn:0022-4812. doi:10.2307/2586556. arXiv:math/9808093. (http://jdh.hamkins.org/ittms)

Joel David Hamkins and Barbara Montero. “Utilitarianism in infinite worlds”. Utilitas 12.1 (2000), pp. 91–96. doi:10.1017/S0953820800002648. (http://jdh.hamkins.org/infiniteworlds)

Joel David Hamkins and Barbara Montero. “With infinite utility, more needn’t be better”. Australasian J. Philosophy 78.2 (2000), pp. 231–240. doi:10.1080/00048400012349511. (http://jdh.hamkins.org/infinite-utility-more-better)

Joel David Hamkins and Simon Thomas. “Changing the heights of automorphism towers”. Ann. Pure Appl. Logic 102.1-2 (2000), pp. 139–157. issn:0168-0072. doi:10.1016/S0168-0072(99)00039-1. arXiv:math/9703204. (http://jdh.hamkins.org/changingheightsoverl)

Joel David Hamkins and W. Hugh Woodin. “Small forcing creates neither strong nor Woodin cardinals”. Proc. Amer. Math. Soc. 128.10 (2000), pp. 3025–3029. issn:0002-9939. doi:10.1090/S0002-9939-00-05347-8. arXiv:math/9808124. (http://jdh.hamkins.org/smallforcing-w)

Arthur W. Apter and Joel David Hamkins. “Universal indestructibility”. Kobe J. Math 16.2 (1999), pp. 119–130. issn:0289-9051. arXiv:math/9808004. (http://wp.me/p5M0LV-12)

Joel David Hamkins. “Gap forcing: generalizing the Lévy-Solovay theorem”. Bulletin of Symbolic Logic 5.2 (1999), pp. 264–272. issn:1079-8986. doi:10.2307/421092. arXiv:math/9901108. (http://jdh.hamkins.org/gapforcinggen)

Joel David Hamkins. “Using video and peer feedback to improve teaching”. Assessment Practices in Mathematics, MAA Notes 49 (1999). Ed. by Bonnie Gold.

Joel David Hamkins. “Destruction or preservation as you like it”. Annals of Pure and Applied Logic 91.2-3 (1998), pp. 191–229. issn:0168-0072. doi:10.1016/S0168-0072(97)00044-4. arXiv:1607.00683. (http://jdh.hamkins.org/asyoulikeit)

Joel David Hamkins. “Every group has a terminating transfinite automorphism tower”. Proc. Amer. Math. Soc. 126.11 (1998), pp. 3223–3226. issn:0002-9939. doi:10.1090/S0002-9939-98-04797-2. arXiv:math/9808014. (http://jdh.hamkins.org/everygroup)

Joel David Hamkins. “Small forcing makes any cardinal superdestructible”. J. Symbolic Logic 63.1 (1998), pp. 51–58. issn:0022-4812. doi:10.2307/2586586. arXiv:1607.00684. (http://jdh.hamkins.org/superdestructibility)

Joel David Hamkins and Saharon Shelah. “Superdestructibility: a dual to Laver’s indestructibility”. J. Symbolic Logic 63.2 (1998). [HmSh:618], pp. 549–554. issn:0022-4812. doi:10.2307/2586848. arXiv:math/9612227. (http://jdh.hamkins.org/dual)

Joel David Hamkins. “Canonical seeds and Prikry trees”. J. Symbolic Logic 62.2 (1997), pp. 373–396. issn:0022-4812. doi:10.2307/2275538. (http://jdh.hamkins.org/seeds)

Joel Hamkins. “Fragile measurability”. J. Symbolic Logic 59.1 (1994), pp. 262–282. issn:0022-4812. doi:10.2307/2275264. (http://jdh.hamkins.org/fragilemeasurability)

Joel David Hamkins. “Lifting and extending measures; fragile measurability”. PhD thesis. Department of Mathematics: University of California, Berkeley, 1994. (http://jdh.hamkins.org/dissertation)

Logic, mathematical logic, philosophical logic, set theory, philosophy of set theory, the mathematics and philosophy of the infinite, infinitary computability, infinitary game theory, infinitary utilitarianism.