We held first seminar on Tuesday, March 20.
Speaker: Maryanthe Malliaris (Hebrew University)
Title: Regular ultrafilters and first-order theories
The talk will present some recent results on regular ultrafilters due to Malliaris and Shelah (Autumn 2011), which have emerged from a program of work of the authors on Keisler’s order, and whose proofs make use of model theory.
Keisler’s order, introduced in 1967, gives a way of comparing the complexity of first-order theories in terms of the difficulty of producing saturated regular ultrapowers. The talk will assume basic knowledge of ultrapowers (Los’ theorem) and model theory (types, saturation). Beyond this, I intend to give all relevant definitions.