Analytic versus Synthetic Consistency Properties

  • Raymond M. Smullyan
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 43)


We have remarked earlier that magic sets emerged from the completeness proofs of Henkin and Hasenjaeger. In this chapter we wish to discuss the Henkin and Hasenjaeger completeness proofs and their relationship to the completeness proofs of earlier chapters. We conclude this chapter with a new proof of the Unifying Principle—which circumvents the necessity of appealing to systematic tableaux—and we discuss the essential differences and similarities of what are basically two types of completeness proofs; the one along the lines of Lindenbaum-Henkin, the other along the lines of Gödel-Herbrand-Gentzen.


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Copyright information

© Springer-Verlag Berlin · Heidelberg 1968

Authors and Affiliations

  • Raymond M. Smullyan
    • 1
  1. 1.Lehman CollegeCity University of New YorkUSA

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