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Forcing: Eine Einfuhrung in die Mathematik der Unabhangigkeitsbeweise

Forcing: Eine Einfuhrung in die Mathematik der Unabhangigkeitsbeweise


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About the Book

Bis in das 20. Jahrhundert hinein war es eine unausgesprochene Grundannahme der Mathematik, dass zwischen der Wahrheit und der Beweisbarkeit einer Aussage nicht unterschieden werden muss. Heute wissen wir, dass diese Sichtweise falsch ist. Es gibt Aussagen, die mit den Mitteln der gewohnlichen Mathematik weder bewiesen noch widerlegt werden konnen. Eine solche Aussage ist die Kontinuumshypothese, mit der Georg Cantor Ende des 19. Jahrhunderts ein Jahrhundertratsel schuf. Die Unentscheidbarkeit der Kontinuumshypothese wurde im Jahr 1963 von Paul Cohen gezeigt, mit einer vollig neuen, als Forcing bezeichneten Beweistechnik. Seitdem haben wir ein machtiges Beweisinstrument in den Handen, mit dem sich nicht nur die Kontinuumshypothese, sondern auch zahlreiche andere mathematische Aussagen, wie z. B. das Auswahlaxiom, als unentscheidbar identifizieren lassen. Das vorliegende Buch ist eine Einfuhrung in die Forcing-Technik, die den Leser in die Lage versetzen soll, die bestehende Literatur zu diesem Thema leichter zu verstehen. Cohens Beweismethode wird Schritt fur Schritt entwickelt und anschließend dazu verwendet, um die Unentscheidbarkeit der Kontinuumshypothese zu belegen. Geschrieben habe ich dieses Buch fur Leser, die bereits uber fundierte mathematische Kenntnisse verfugen, aber keine Experten im Bereich der Mengenlehre oder Logik sind. Das Buch kann unabhangig von Vorlesungen auch zum Selbststudium genutzt werden. Alle Kapitel sind mit zahlreichen Ubungsaufgaben versehen, deren Losungen im Internet abgerufen werden konnen.


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Product Details
  • ISBN-13: 9783746044606
  • Publisher: Books on Demand
  • Binding: Hardcover
  • Language: German
  • Width: 913.999 mm
  • ISBN-10: 374604460X
  • Publisher Date: 2/22/2018
  • Height: 226 mm
  • Weight: 31 gr


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