Cardinals that might be viewed as miniature superstrong cardinals consistent with V=L

Set theory seminarFriday, February 22, 201312:00 amRoom 5383

Thomas Johnstone

Cardinals that might be viewed as miniature superstrong cardinals consistent with V=L

The New York City College of Technology (CityTech), CUNY

We will discuss cardinals that we may call superstrongly unfoldable cardinals. A cardinal kappa is superstrongly unfoldable if it is theta-superstrongly unfoldable for every ordinal theta, meaning that for subset A of kappa there is a nontrivial elementary embedding j:M–>N between transitive ZFC models having critical point kappa such that j(kappa)>theta and V_{j(kappa)} is a subset of N and the set A is an element of M. Superstrongly unfoldable cardinals lie in consistency strength between weakly compact cardinals and Ramsey cardinals, and they are relatively consistent with V=L. We will show the tighter consistency bounds of strongly unfoldable cardinals below and subtle cardinals above. This is joint work with Joel David Hamkins.

Thomas Johnstone is a professor of mathematics at the New York City College of Technology (City Tech), CUNY. His research in Set Theory includes large cardinals, forcing, and indestructibility.

Posted by on February 20th, 2013