# Chris Eagle: Omitting types in infinitary $[0, 1]$-valued logic

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 $\mathcal{L}_{\omega_1, \omega}$.