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397:. 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.
299:, 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
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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
290:, 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
333:, 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
337:. 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
274:, 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."
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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
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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
573:, 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
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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.).
498:"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".
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585:, World Science Festival, New York City, June 1, 2013. (Hamkins was a panelist.)
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C. D. A. Evans and J. D. Hamkins, "Transfinite game values in infinite chess,"
1159:. 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-
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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.
624:, Science News, Volume 164, Number 9, August 30, 2003, page 139.
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The Future of Infinity: Solving Math's Most Notorious Problem
174:
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Hamkins, Joel David (2012). "The set-theoretic multiverse".
512:"Notre Dame Hires Hamkins from Oxford and Montero from CUNY"
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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.
1225:, doi: 10.5281/zenodo.10075843, arXiv:2201.06475.
1120:"Every group has a terminating automorphism tower"
307:In his philosophical work, Hamkins has defended a
724:Transactions of the American Mathematical Society
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248:In September 2018, Hamkins moved to the
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496:Hamkins, Joel David (May 17, 2018).
211:University of California at Berkeley
205:and professor of mathematics at the
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171:California Institute of Technology
54:California Institute of Technology
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769:The Journal of Symbolic Logic
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636:The Journal of Symbolic Logic
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347:infinite-time Turing machines
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197:He joined the faculty of the
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1118:Hamkins, Joel David (1998).
948:The Review of Symbolic Logic
859:The Review of Symbolic Logic
611:New Scientist, 26 June 2013.
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1326:Interview at 3AM Magazine,
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349:, a part of the subject of
199:City University of New York
93:City University of New York
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341:Infinitary computability
303:Philosophy of set theory
258:University of Notre Dame
227:Georgia State University
207:College of Staten Island
147:set-theoretic multiverse
131:University of Notre Dame
115:José R. Ramírez-Garofalo
85:University of Notre Dame
1274:The Global Math Commons
1221:, volume 23, paper G6,
363:generic-case complexity
231:University of Amsterdam
1328:Playing infinite chess
1237:, by reputation score.
596:Playing Infinite Chess
526:Google Scholar profile
355:descriptive set theory
353:, with connections to
264:Research contributions
243:Isaac Newton Institute
169:in mathematics at the
16:American mathematician
223:University of Münster
173:, Hamkins earned his
550:The Span of Infinity
514:. 23 September 2021.
447:"Joel David Hamkins"
313:Continuum Hypothesis
250:University of Oxford
203:CUNY Graduate Center
151:computability theory
89:University of Oxford
791:10.2178/jsl.7801090
409:juggling notation.
239:New York University
167:Bachelor of Science
139:philosophical logic
1364:American logicians
1317:Joel David Hamkins
1302:Joel David Hamkins
1235:MathOverflow users
1208:. arXiv:2111.02053
594:Richard Marshall,
127:Joel David Hamkins
23:Joel David Hamkins
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1130:(11): 3223–3226.
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