The notion of a scattered sentence of L_{omega_1,omega} is due to Morley and is in response to his work on Vaught’s conjecture, where he showed that a scattered sentence has at most aleph_1 many nonisomorphic countable models, whereas a non-scattered sentence has continuum many nonisomorphic countable models. Keisler showed some interesting connections between scattered sentences and randomizations. Indeed, he showed that if a sentence has “few” separable randomizations, then it is scattered, and the converse holds under Martin’s axiom. I will discuss this result as well as the removal of Martin’s axiom, which is joint work with Andrews, Hachtman, Keisler, and Marker.
We will have tea from 3pm in the Huxley comon room.