@MISC{GOEDCPUC.MIZ,
  AUTHOR = {Schl\"oder, Julian J. and Koepke, Peter},
  TITLE = {The G\"odel Completeness Theorem for Uncountable Languages},
  NOTE = {This article is part of the first authors Bachelor thesis under the supervision of the second author.},
  SECTION1 = {Formula-Constant Extension},
  SECTION2 = {The Completeness Theorem},
  DAY = {7},
  MONTH = {May},
  YEAR = {2012},
  ADDRESS1 = {Mathematisches Institut\\Rheinische Friedrich-Wilhelms-Universit\"at Bonn\\Endenicher Allee 60\\D-53113 Bonn\\Germany},
  ADDRESS2 = {Mathematisches Institut\\Rheinische Friedrich-Wilhelms-Universit\"at Bonn\\Endenicher Allee 60\\D-53113 Bonn\\Germany},
  SUMMARY = {This article is the second in a series
  of two Mizar articles constituting a formal
  proof of the G\"odel Completeness theorem
  \cite{G\"odel:1930)} for uncountably large
  languages. We follow the proof given in \cite{Ebbinghaus2007}.
  The present article contains the techniques required to expand
  a theory such that the expanded theory contains witnesses
  and is negation faithful. Then the completeness theorem
  follows immediately.}}
