  We find necessary and sufficient conditions for a complete local (Noetherian)
ring to be the completion of an uncountable local (Noetherian) domain with a
countable spectrum. Our results suggest that uncountable local domains with
countable spectra are more common than previously thought. We also characterize
completions of uncountable excellent local domains with countable spectra
assuming the completion contains the rationals, completions of uncountable
local unique factorization domains with countable spectra, completions of
uncountable noncatenary local domains with countable spectra, and completions
of uncountable noncatenary local unique factorization domains with countable
spectra.
