Speaker:
Dr Sean Cox
Institution:
University of Muenster, Gemany
Time:
Monday, September 26, 2011 - 4:00pm
Location:
RH 440R
I will discuss the Diagonal Reflection Principle (DRP), which is a highly simultaneous form of stationary set reflection that follows from strong forcing axioms like $PFA^{+\omega_1}$. DRP can be viewed as a weaker version of the statement "there is a normal ideal with completeness $\omega_2$ whose associated poset is proper (i.e. preserves stationary subsets of $[X]^\omega$ for all $X$)". In the presence of sufficiently absolute partitions of $cof(\omega)$, such ideals yield generic embeddings $j: V \to_G ult(V,G)$ with critical point $\omega_2$ such that large portions of $j$ are visible to $V$.