@MISC{QC_TRANS.MIZ,
  AUTHOR = {Schl\"oder, Julian J. and Koepke, Peter},
  TITLE = {Transition of Consistency and Satisfiability under
     Language Extensions},
  NOTE = {This article is part of the first authors Bachelor
     thesis under the supervision of the second author.},
  SECTION1 = {Language Extensions},
  SECTION2 = {Downward Transfer of Consistency and Satisfiability},
  SECTION2 = {Upward Transfer of Consistency and Satisfiability},
  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 first in a series of two Mizar
    articles constituting a formal proof of the Gödel Completeness
    theorem \cite{Goedel:1930)} for uncountably large languages.
    We follow the proof given in \cite{Ebbinghaus2007}.
    The present article contains the techniques
    required to expand formal languages. We prove that consistent
    or satisfiable theories retain these properties under changes to
    the language they are formulated in.}}

@BOOK{Ebbinghaus2007,
 AUTHOR={H.-D. Ebbinghaus, J. Flum, W. Thomas},
 TITLE = {Einf\"uhrung in die Mathematische Logik},
 YEAR = {2007},
 PUBLISHER = {Springer-Verlag, Berlin Heidelberg}}

@BOOK{Goedel:1930,
 AUTHOR={G\"odel, Kurt},
 TITLE={Die Vollständigkeit der Axiome des logischen Funktionenkalk\"uls},
 PUBLISHER={Monatshefte f\"ur Mathematik und Physik 37},
 YEAR=1930}}

