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The continuum problem and forcing

  • Yu. I. Manin
Part of the Graduate Texts in Mathematics book series (GTM, volume 53)

Abstract

Cantor introduced two fundamental ideas in the theory of infinite sets: he discovered (or invented?) the scale of cardinalities of infinite sets, and gave a proof that this scale is unbounded. We recall that two sets M and N are said to have the same cardinality (card M = card N) if there exists a one-to-one correspondence between them. We write card M⩽ card N if M has the same cardinality as a subset of N. We say that M and N are comparable if either card M ⩽ card N or card N ⩽ card M. We write card M > card N if card M ⩾ card N but M and N do not have the same cardinality.

Keywords

Boolean Algebra Atomic Formula Continuum Problem Continuum Hypothesis Complete Boolean Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1977

Authors and Affiliations

  • Yu. I. Manin
    • 1
  1. 1.V. A. Steklov Mathematical Institute of the Academy of SciencesMoscowUSSR

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