Title: Rudolph's Thesis.
Abstract: This talk presents a general method of showing that different natural contexts for probability measure preserving transformations have the same generic properties. The key definition is that of a model for the measure preserving transformations. A short Vaught's-transform argument shows that any two models have the same generic properties. This validates a meta-conjecture of Rudolph that all natural settings for measure preserving transformations have the same properties.
Examples will be given: the Glasner-King Theorem about Shift-Invariant measures on $[0,1]^\poZ$, the Rudolph theorem on $O(T)$, the space of transformations orbit equivalent to an ergodic $T$ as well as new examples: the space of shift invariant measures on $\Sigma^\poZ$ that give basic open sets rational measure, the space of interval exchanges on $[0,1]$ and finally an example of a space that does not have the same generic transformations: the rational interval exchanges on $[0,