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Mar 19, 2011 at 19:10 comment added Pete L. Clark @Mark: right, I had that thought as well, but was hoping for something a little simpler...like Moret-Bailly's response below.
Mar 19, 2011 at 10:17 comment added user6976 I do not have time, but you can use the fact that (at least assuming Continuum Hypothesis) every ultraproduct is saturated.
Mar 19, 2011 at 5:42 comment added Pete L. Clark This is correct, but having seen this counterexample it is natural to ask about extensions of infinite ultrafields. Isn't the answer still negative?
Mar 19, 2011 at 3:42 history edited user6976 CC BY-SA 2.5
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Mar 19, 2011 at 2:08 history answered user6976 CC BY-SA 2.5