I have been searching the web for several years now attempting to find a good intuitive explanation of what measurable cardinals are and how best to conceive them. All I can find, over nd over, are definitions of the things in terms of ultrafilters and k-sigma measures. I do know what those things are, but that doesn't help me visualize what a measurable cardinal looks like, how one makes one, or why it has the properties it does. Can anyone help me with this?? Thanks for reading!!