**May 6**

James Holland,
Rutgers University

**Weak Indestructibility and Reflection**

Assuming multiple of strong cardinals, there are lots of cardinals with small degrees of strength (i.e. $\kappa$ that are $\kappa$+2-strong). We can calculate the consistency strength of these all cardinal's small degrees of strength being weakly indestructible using forcing and core model techniques in a way similar to Apter and Sargsyan's previous work. This yields some easy relations between indestructibility and Woodin cardinals, and also generalizes easily to supercompacts. I will give a proof sketches of these results.