We will review the construction of an ultrapower embedding from V into an inner model using a measurable cardinal κ and show that κ is the critical point of this embedding. Conversely, we will show that every nontrivial embedding has a critical point and sketch the argument that this critical point is measurable. Finally, we will use a normal measure on such a κ to prove that measurable cardinals are Ramsey in the very strong sense that the homogeneous set is not only of large cardinality but is large with respect to the measure.
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