A Course in Mathematical Logic pp 103-148 | Cite as

# The continuum problem and forcing

Chapter

## 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