Fri May 4, 2007
60 Evans Hall, 4:10–6 PM
John R. Steel (UC-Berkeley)
A Correctness Result for Canonical Inner Models
One of the most basic features of the canonical inner models for large cardinal hypotheses is that their elements are all ordinal definable. The larger the model M, the greater the logical complexity required to define the elements of M. On the other hand, the larger the model M, the greater the logical complexity of the formulas whose truth in V can be determined inside M. For the most natural M, complexity and correctness keep pace, so that M satisfies “Every set is ordinal definable”. Although this is not true for all canonical inner models M, it is possible that every M satisfies “T here is a real from which all reals are ordinal definable”. We shall discuss a partial result in this direction.