October 12
Roman Kossak,
CUNY
Full Satisfaction
A full satisfaction class for a model of Peano Arithmetic is an assignment of truth values to all sentences in the sense of the model that respects Tarski's inductive conditions for satisfaction relation. In 1976, Lachlan proved that every model of PA that has a full satisfaction class is recursively saturated. Lachlan's construction is intricate. Recently, Bartosz Wcisło developed a general method based on Lachlan's argument that allowed him to show that if a model has a full satisfaction class, then it also has a partial inductive satisfaction class, improving a previous result by Stuart Smith. I will outline Wcisło's method, and I'll survey some related results.