Blog Archives

Topic Archive: tall cardinals

Set theory seminarFriday, April 15, 201611:00 amGC 6417

Arthur W. Apter

Normal Measures and Tall Cardinals

The City University of New York

I will discuss the number of normal measures a non-$(\kappa + 2)$-strong tall cardinal $\kappa$ can carry, paying particular attention to the cases where $\kappa$ is either the least measurable cardinal or the least measurable limit of strong cardinals. This is joint work with James Cummings.


Set theory seminarFriday, February 20, 201511:00 amGC 6417

Arthur W. Apter

The tall and measurable cardinals can coincide on a proper class

The City University of New York

Starting from an inaccessible limit of strong cardinals, we force to construct a model containing a proper class of measurable cardinals in which the tall and measurable cardinals coincide precisely. This is joint work with Moti Gitik which extends and generalizes an earlier result of Joel Hamkins.


Joel David Hamkins
The City University of New York
Professor Hamkins (Ph.D. 1994 UC Berkeley) conducts research in mathematical and philosophical logic, particularly set theory, with a focus on the mathematics and philosophy of the infinite.  He has been particularly interested in the interaction of forcing and large cardinals, two central themes of contemporary set-theoretic research.  He has worked in the theory of infinitary computability, introducing (with A. Lewis and J. Kidder) the theory of infinite time Turing machines, as well as in the theory of infinitary utilitarianism and, more recently, infinite chess.  His work on the automorphism tower problem lies at the intersection of group theory and set theory.  Recently, he has been preoccupied with various mathematical and philosophical issues surrounding the set-theoretic multiverse, engaging with the emerging debate on pluralism in the philosophy of set theory, as well as the mathematical questions to which they lead, such as in his work on the modal logic of forcing and set-theoretic geology.