continuum hypothesis sentence in Hindi
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- The continuum hypothesis and the axiom of choice were among the first mathematical statements shown to be independent of ZF set theory.
- The last step in showing the independence of the continuum hypothesis, then, is to show that Cohen forcing does not collapse cardinals.
- This is a generalization of the continuum hypothesis since the continuum has the same cardinality as the power set of the integers.
- For example, if the Continuum Hypothesis holds then every countable model has an ultrapower which is saturated ( in its own cardinality ).
- It is also not complete, as illustrated by the in ZFC + " there exists an inaccessible cardinal " theory unresolved continuum hypothesis.
- The continuum hypothesis, first proposed as a conjecture by Cantor, was listed by David Hilbert as one of his 23 problems in 1900.
- In the view of some, then, it is equally reasonable to take either the continuum hypothesis or its negation as a new axiom.
- This is especially the case with some of the key notions discussed by Aczel, namely the continuum hypothesis and the axiom of choice.
- In the multiverse view it is meaningless to ask whether the continuum hypothesis is true or false before selecting a model of set theory.
- A trivial consequence of the continuum hypothesis is that a complete theory with less than continuum many nonisomorphic countable models can have only countably many.
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