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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis

[denial of a cardinality between naturals are reals]

15 ideas
The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro]
CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner]
Cantor: there is no size between naturals and reals, or between a set and its power set [Cantor, by Hart,WD]
Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers [Cantor, by Horsten]
Continuum Hypothesis: there are no sets between N and P(N) [Cantor, by Wolf,RS]
Continuum Hypothesis: no cardinal greater than aleph-null but less than cardinality of the continuum [Cantor, by Chihara]
The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
The undecidability of the Continuum Hypothesis may have ruined or fragmented set theory [Badiou]
The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M]
Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
The 'continuum' is the cardinality of the powerset of a denumerably infinite set [Shapiro]
The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg]
The Continuum Hypothesis is independent of the axioms of set theory [Clegg]