Ultraproducts and Los' Theorem

Fill the blank to complete the following definition of an ultrafilter.

An ultrafilter on a set I is a filter on I that is ______ with respect to set inclusion.

A principal ultrafilter on I is an ultrafilter U such that.

• An ultrafilter on I that such that the resulting ultrapowers are isomorphic to the component structures.

• One that is equivalent to a principal ideal domain.

Which of the properties of filters is used in the existential case of the proof of Los' theorem?

What kind of proof is used in Los' Theorem.

• True

• False

• I do not know.

• True

• False

• I do not know.

• True

• False

• I do not know.

• True

• False

• I do not know.

• True

• False

• I do not know.