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408:. Hamkins and Evans investigated transfinite game values in infinite chess, proving that every countable ordinal arises as the game value of a position in infinite three-dimensional chess. Hamkins and Davide Leonessi proved that every countable ordinal arises as a game value in infinite draughts. They also proved that infinite Hex is a draw.
310:, which asserts that the set-theoretic universe is not a forcing extension of any inner model by set forcing. Hamkins proved that any two countable models of set theory are comparable by embeddability, and in particular that every countable model of set theory embeds into its own constructible universe.
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that if ZFC is consistent, then the ZFC-provably valid principles of forcing are exactly those in the modal theory known as S4.2. Hamkins, Linetsky and Reitz proved that every countable model of Gödel-Bernays set theory has a class forcing extension to a pointwise definable model, in which every set
331:
writes of
Hamkins's work on the set-theoretic multiverse that, "the resulting study is an array of new fantastic, and sometimes bewildering, concepts and results that already have yielded a flowering of what amounts to a new branch of set theory. This ground-breaking paper gives us a glimpse of the
301:, proving that small forcing necessarily ruins the indestructibility of supercompact and other large cardinals and introducing the lottery preparation as a general method of forcing indestructibility. Hamkins introduced the modal logic of forcing and proved with
344:, he introduced several varieties of set-theoretic potentialism. He gave a similar analysis for potentialist concepts in arithmetic, treating the models of PA under a variety of natural extension concepts, using especially the universal algorithm of
348:. In further joint work, Hamkins and Woodin provided a set-theoretic generalization of that result. Hamkins mounted a general account of modal model theory in joint work with his Oxford DPhil student Wojciech Aleksander Wołoszyn.
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In other computability work, Hamkins and
Miasnikov proved that the classical halting problem for Turing machines, although undecidable, is nevertheless decidable on a set of asymptotic probability one, one of several results in
285:, as part of an ongoing interview series for that magazine of prominent philosophers and public intellectuals, and he is occasionally interviewed by the popular science media about issues in the philosophy of mathematics.
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question, for example, "is settled on the multiverse view by our extensive knowledge about how it behaves in the multiverse, and as a result it can no longer be settled in the manner formerly hoped for." (Hamkins 2012)
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Hamkins has investigated several infinitary games, including infinite chess, infinite draughts, infinite Hex, and others. On the topic of infinite chess, Hamkins, Brumleve and
Schlicht proved that the mate-in-
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describes him as "one of those distinguished mathematicians whose arrays of MO answers in their areas of interest draw coherent deep pictures for these areas that you probably cannot find anywhere else."
322:
perspective of mathematical truth, arguing that diverse concepts of set give rise to different set-theoretic universes with different theories of mathematical truth. He argues that the
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J. D. Hamkins, plenary
General Public Lecture, Higher infinity and the Foundations of Mathematics, American Association for the Advancement of Science, Pacific Division, June, 2014.
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As an undergraduate at
Caltech in the 1980s, Hamkins made contributions to the mathematical theory of juggling, working with Bruce Tiemann to develop what became known as the
385:
1168:
How the World
Computes – Turing Centenary Conference and 8th Conference on Computability in Europe, CiE 2012, Cambridge, United Kingdom, June 18–23, 2012. Proceedings
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Hamkins research work is cited, and he gives talks, including events for the general public. Hamkins was interviewed on his research by
Richard Marshall in 2013 for
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Hamkins, Joel David; Linnebo, Øystein (2022). "THE MODAL LOGIC OF SET-THEORETIC POTENTIALISM AND THE POTENTIALIST MAXIMALITY PRINCIPLES".
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Hamkins, Joel David; Miasnikov, Alexei (2006). "The
Halting Problem Is Decidable on a Set of Asymptotic Probability One".
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in 1995, where he was a member of the doctoral faculties in
Mathematics, in Philosophy and in Computer Science at the
584:, The Intrinsic Value Project, Underground Zero, New York City, July 9 & 10, 2014. (Hamkins was a panelist.)
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Hamkins, Joel David (2013). "Every countable model of set theory embeds into its own constructible universe".
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Hamkins has investigated a model-theoretic account of the philosophy of potentialism. In joint work with
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to become
Professor of Logic in the Faculty of Philosophy and Sir Peter Strawson Fellow in Philosophy in
209:
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Hamkins, Joel David (2013). "David Linetsky and Jonas Reitz, Pointwise definable models of set theory".
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In group theory, Hamkins proved that every group has a terminating transfinite automorphism tower. With
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is an American mathematician and philosopher who is the John Cardinal O'Hara Professor of Logic at the
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problem of infinite chess is decidable". In Cooper, S. Barry; Dawar, Anuj; Löwe, Benedikt (eds.).
509:"Oxford University, Professor of Logic & Sir Peter Strawson Fellow, University College Oxford"
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Joel David Hamkins and Davide Leonessi. "Transfinite game values in infinite draughts,"
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J. D. Hamkins, The multiverse perspective on determinateness in set theory, talk at the
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Hamkins, Joel David (1998). "Small Forcing Makes any Cardinal Superdestructible".
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Hamkins, Joel David; Wołoszyn, Wojciech Aleksander (2022). "Modal model theory".
225:
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1185:
596:, World Science Festival, New York City, June 1, 2013. (Hamkins was a panelist.)
1198:
C. D. A. Evans and J. D. Hamkins, "Transfinite game values in infinite chess,"
1170:. Lecture Notes in Computer Science. Vol. 7318. Springer. pp. 78–88.
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A Meeting at the Crossroads - Science, Performance and the Art of Possibility
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and class is definable without parameters. Hamkins and Reitz introduced the
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Brumleve, Dan; Hamkins, Joel David; Schlicht, Philipp (2012). "The mate-in-
429:
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Hamkins, Joel David; Lewis, Andy (2000). "Infinite-time Turing machines".
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Hamkins, Joel David; Löwe, Benedikt (2008). "The modal logic of forcing".
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amazingly fecund developments spearheaded by the author and...others..."
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showing that a difficult or unsolvable problem can be easy on average.
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Zentralblatt review of J. D. Hamkins, The set-theoretic multiverse,
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Joel David Hamkins and Davide Leonessi. "Infinite Hex is a draw,"
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of Hamkins breaking 100,000 reputation score, September 17, 2014.
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Hamkins introduced with Jeff Kidder and Andy Lewis the theory of
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Lifting and Extending Measures by Forcing; Fragile Measurability.
635:, Science News, Volume 164, Number 9, August 30, 2003, page 139.
594:
The Future of Infinity: Solving Math's Most Notorious Problem
185:
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Hamkins, Joel David (2012). "The set-theoretic multiverse".
523:"Notre Dame Hires Hamkins from Oxford and Montero from CUNY"
156:
and philosophy of set theory (particularly the idea of the
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on Hamkins's MathOverflow achievements, January 29, 2014.
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Hamkins, Joel David (2000). "The Lottery Preparation".
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Mathematicians Think Like Machines for Perfect Proofs
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Hamkins is the top-rated user by reputation score on
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of Hamkins posting 1000th answer, January 30, 2014.
1236:, doi: 10.5281/zenodo.10075843, arXiv:2201.06475.
1131:"Every group has a terminating automorphism tower"
318:In his philosophical work, Hamkins has defended a
735:Transactions of the American Mathematical Society
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271:as the John Cardinal O'Hara Professor of Logic.
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293:In set theory, Hamkins has investigated the
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1390:California Institute of Technology alumni
1370:University of California, Berkeley alumni
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259:In September 2018, Hamkins moved to the
1202:, volume 14, Paper Number G2, 36, 2014.
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507:Hamkins, Joel David (May 17, 2018).
222:University of California at Berkeley
216:and professor of mathematics at the
937:, 5, Number 3, pages 416-449 (2012)
24:
996:Notre Dame Journal of Formal Logic
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267:. In January 2022 he moved to the
190:University of California, Berkeley
182:California Institute of Technology
65:California Institute of Technology
61:University of California, Berkeley
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780:The Journal of Symbolic Logic
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712:10.1016/S0168-0072(99)00010-X
647:The Journal of Symbolic Logic
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358:infinite-time Turing machines
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208:He joined the faculty of the
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959:The Review of Symbolic Logic
870:The Review of Symbolic Logic
622:New Scientist, 26 June 2013.
171:
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1337:Interview at 3AM Magazine,
1186:10.1007/978-3-642-30870-3_9
360:, a part of the subject of
210:City University of New York
104:City University of New York
10:
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1086:Notre Dame J. Formal Logic
1018:10.1215/00294527-2024-0001
551:, from Hamkins's web page.
265:University College, Oxford
230:Carnegie Mellon University
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352:Infinitary computability
314:Philosophy of set theory
269:University of Notre Dame
238:Georgia State University
218:College of Staten Island
158:set-theoretic multiverse
142:University of Notre Dame
126:José R. Ramírez-Garofalo
96:University of Notre Dame
1285:The Global Math Commons
1232:, volume 23, paper G6,
374:generic-case complexity
242:University of Amsterdam
1339:Playing infinite chess
1248:, by reputation score.
607:Playing Infinite Chess
537:Google Scholar profile
366:descriptive set theory
364:, with connections to
275:Research contributions
254:Isaac Newton Institute
180:in mathematics at the
27:American mathematician
234:University of Münster
184:, Hamkins earned his
561:The Span of Infinity
525:. 23 September 2021.
458:"Joel David Hamkins"
324:Continuum Hypothesis
261:University of Oxford
214:CUNY Graduate Center
162:computability theory
100:University of Oxford
802:10.2178/jsl.7801090
420:juggling notation.
250:New York University
178:Bachelor of Science
150:philosophical logic
1375:American logicians
1328:Joel David Hamkins
1313:Joel David Hamkins
1246:MathOverflow users
1219:. arXiv:2111.02053
605:Richard Marshall,
138:Joel David Hamkins
34:Joel David Hamkins
1283:Erica Klarreich,
1141:(11): 3223–3226.
929:Elliott Mendelson
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484:"Curriculum Vita"
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