Postscript: The Impact of Mathematical Logic

  • Bruce Chandler
  • Wilhelm Magnus
Part of the Studies in the History of Mathematics and Physical Sciences book series (HISTORY, volume 9)


In all of the previous chapters we have dealt with developments which started before the middle of the Twentieth Century, although, in many cases, we also reported on some of their later phases. In the present chapter we are making an exception to this rule which we imposed on our account in order to keep it from becoming too voluminous. Our reason for doing so is the exceptional nature of the impact of mathematical logic on combinatorial group theory. We encounter here the situation where concepts and methods from one mathematical discipline become essential ingredients of the theorems and of the answers to previously open questions of another discipline. Of course, events of this type have happened before, but they deserve to be mentioned with distinction. In a way, the connection between topology and combinatorial group theory provides a similar example. However, there exists a notable difference between these two occurrences. Topology and combinatorial group theory grew up together, but the event we are now going to describe involves the action of a highly developed sophisticated theory on another equally developed discipline.


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Copyright information

© Springer-Verlag New York Inc. 1982

Authors and Affiliations

  • Bruce Chandler
    • 1
  • Wilhelm Magnus
    • 2
  1. 1.The College of Staten Island of The City University of New YorkStaten IslandUSA
  2. 2.New RochelleUSA

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