We argue that the existence of solitons in theories in which local symmetries are spontaneously broken requires spacetime to be enlarged by additional coordinates that are associated with large local transformations. In the context of gravity theories the usual coordinates of spacetime can be thought of arising in this way. E theory automatically contains such an enlarged spacetime. We propose that spacetime appears in an underlying theory when the local symmetries are spontaneously broken.

Affine logic is the fragment of continuous logic in which the connectives are limited to affine functions. I will discuss the basics of this logic, first studied by Bagheri, and present the results of a recent joint work with I. Ben Yaacov and T. Tsankov in which we initiate the study of extreme types and extremal models in affine logic.

In particular, I will discuss an extremal decomposition result for models of simplicial affine theories, which generalizes the ergodic decomposition theorem.