more from Michael Hallett

### Single Idea 17836

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis]

Full Idea

In 1938, Gödel showed that ZF plus the General Continuum Hypothesis is consistent if ZF is. Cohen showed that ZF and not-GCH is also consistent if ZF is, which finally shows that neither GCH nor ¬GCH can be proved from ZF itself.

Gist of Idea

The General Continuum Hypothesis and its negation are both consistent with ZF

Source

Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1217)

Book Reference

'From Kant to Hilbert: sourcebook Vol. 2', ed/tr. Ewald,William [OUP 1996], p.1217