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/) Citation arχiv...
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Every countable model of set theory embeds into its own constructible...
This will be a talk for the Toronto set theory seminar at the Fields Institute, University of Toronto, on August 24, 2012. Abstract. Every countable model of set theory $M$, including every...
View ArticleMoving 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. Journal Citation arχiv...
View ArticleRecent progress on the modal logic of forcing and grounds, CUNY Logic...
This will be a talk for the CUNY Logic Workshop on September 7, 2012. Abstract. The modal logic of forcing arises when one considers a model of set theory in the context of all its forcing extensions,...
View ArticleA question for the mathematics oracle
At the Workshop on Infinity and Truth in Singapore last year, we had a special session in which the speakers were asked to imagine that they had been granted an audience with an all-knowing...
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Every countable model of set theory is isomorphic to a submodel of its own...
This will be a talk for a set theory workshop at the University of Barcelona on December 15, 2012, organized by Joan Bagaria. Abstract. Every countable model of set theory $M$, including every...
View ArticleA multiverse perspective on the axiom of constructiblity
J. D. Hamkins, “A multiverse perspective on the axiom of constructibility, in Infinity and Truth.” , 2013, vol. 25. Citation arχiv @INBOOK{Hamkins2013:MultiverseOnVeqL, author = {Joel David...
View ArticlePluralism in set theory: does every mathematical statement have a definite...
This will be my talk for the CUNY Graduate Center Philosophy Colloquium on November 28, 2012. I will be speaking on topics from some of my recent articles: The set-theoretic multiverse The multiverse...
View ArticleOn the axiom of constructibility and Maddy’s conception of restrictive...
This is a talk for the CUNY Logic Workshop on February 15, 2013. This talk will be based on my paper, A multiverse perspective on the axiom of constructibility. Set-theorists often argue against the...
View ArticlePluralism in mathematics: the multiverse view in set theory and the question...
This is a talk for the Rutgers Logic Seminar on March 25th, 2013. Simon Thomas specifically requested that I give a talk aimed at philosophers. Abstract. I shall describe the debate on pluralism in...
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A multiverse perspective in mathematics and set theory: does every...
This will be a talk for specialists in philosophy, mathematics and the philosophy of mathematics, given as part of the workshop Metamathematics and Metaphysics, June 15, 2013, sponsored by the group in...
View ArticleExploring the Frontiers of Incompleteness, Harvard, August 2013
I will be participating in the culminating workshop of the Exploring the Frontiers of Incompleteness conference series at Harvard University, to take place August 31-September 1, 2013. Rather than...
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Satisfaction is not absolute
J. D. Hamkins and R. Yang, “Satisfaction is not absolute,” , pp. 1-34. (manuscript under review) Citation arχiv @ARTICLE{HamkinsYang:SatisfactionIsNotAbsolute, author = {Joel David Hamkins and...
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Higher infinity and the foundations of mathematics, plenary General Public...
I have been invited to give a plenary General Public Lecture at the 95th annual meeting of the American Association for the Advancement of Science (Pacific Division), which will be held in Riverside,...
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The pluralist perspective on the axiom of constructibility, MidWest PhilMath...
This will be a featured talk at the Midwest PhilMath Workshop 15, held at Notre Dame University October 18-19, 2014. W. Hugh Woodin and I will each give one-hour talks in a session on Perspectives on...
View ArticleUpward closure in the generic multiverse of a countable model of set theory,...
This will be a talk for the conference Recent Developments in Axiomatic Set Theory at the Research Institute for Mathematical Sciences (RIMS) in Kyoto, Japan, September 16-18, 2015. Abstract. Consider...
View ArticleBeing HOD-of-a-set is invariant throughout the generic multiverse
$\newcommand\HOD{\text{HOD}}$The axiom $V=\HOD$, introduced by Gödel, asserts that every set is ordinal definable. This axiom has a subtler foundational aspect than might at first be expected. The...
View ArticleUpward closure and amalgamation in the generic multiverse of a countable...
[bibtex key=Hamkins:UpwardClosureAndAmalgamationInTheGenericMultiverse] Continue reading →
View ArticleThe modal logic of set-theoretic potentialism and the potentialist maximality...
[bibtex key="HamkinsLinnebo:Modal-logic-of-set-theoretic-potentialism"] Continue reading →
View ArticleNonamalgamation in the Cohen generic multiverse, CUNY Logic Workshop, March 2018
This will be a talk for the CUNY Logic Workshop on March 23, 2018, GC 6417 2-3:30pm. Abstract. Consider a countable model of set theory $M$ in the context of all its successive forcing extensions and...
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