Computability Learning Seminar

Michael Deveau, Department of Pure Mathematics, University of Waterloo

"Scott Sentences for Existentially Atomic Structures"

We have seen the existence of a Scott family comprised of existential formulas for a structure is equivalent to the that structure being existentially atomic. We can now define the equivalent notion for a single (infinite) sentence, and prove that possessing such a sentence is also equivalent to the structure being existentially atomic. As per usual, we will also prove an effective version.

MC 5403