Notes from Lecture 4: Ultrafilter Extensions and the Standard Translation

u1 = {Z | there are finitely many sets X1, . . . Xk such that Z = X1 ∩ · · · ∩Xk}. That is, u1 is the set of finite intersections of sets from u0. Note that u0 ⊆ u1, since u0 has the finite intersection property, we have ∅ 6∈ u1, and by definition u1 is closed under finite intersections. Now, define u2 as follows: u′ = {Y | there is a Z ∈ u1 such that Z ⊆ Y } ∗UMD, Philosophy. Webpage: ai.stanford.edu/∼epacuit, Email: [email protected]