8/March/2013, 13:30–15:00

Fields institute,Room 210

Speaker: Chris Eagle

Title: Omitting types in infinitary $[0, 1]$-valued logic.

Abstract: In first-order logic many interesting non-elementary classes of

mathematical structures can be classified by the types that they realize

or omit. The classical Omitting Types Theorem characterizes those types

which can be omitted in models of a fixed theory $T$ as the ones which are

not generated over $T$ by a single formula. The Omitting Types Theorem

has close connections to the Baire Category Theorem, which we will use to

give a topological proof of an Omitting Types Theorem for a logic for

metric structures which is analogous to $\mathcal{L}_{\omega_1, \omega}$.