Speaker: Robert Owen (University of Wisconsin-Madison)

Title: Outer models, class forcing, and weakly self-defining classes

Abstract: M.C. Stanley described [1] a notion of class forcing that allows 
$0^\sharp$ to be realized from a ground model of $V=L$ assuming such 
models exist in the universe.  We consider the Definability Lemma for such 
forcings and use this as a springboard to discuss set-theoretic complexity 
classes lying between $\Sigma_n$/$\Pi_n$ and $\Delta_{n+1}$, and their 
self-definability.

[1] M. C. Stanley: Outer models and genericity. J. Symb. Log. 68(2): 
389-418 (2003)