Time:  12:00  13:20 
Room: 
PPB 300 (next to Facilities Management Services)

Speaker: 
William Boney CMU 
Title: 
Logic with the quantifier "there exist uncountably many"

Abstract:  First order logic provides us the ability to talk about properties shared by all elements or properties that at least one element has. However, there is plenty of room in between all and one; namely, many. One way of capturing many is to add a quantifier whose intended meaning is that M \models Qx \phi(x) iff  \phi(M)  \geq \aleph_1. Following Keisler's paper of the same name, we present the basics of the model theory of L(Q) including (depending on time) the syntax of L(Q), completeness, an omitting types theorem, and a result on the number of models of size \omega_1. 