Paul Cohen, 1934-2007

Alexandre Borovik is reporting that Paul Cohen has died. Cohen of course proved that the continuum hypothesis is independent of the axioms of set theory, and that the axiom of choice was independent of the other axioms.

Gödel had already established that both the continuum hypothesis and axiom of choice were consistent, in the sense if you could derive a contradiction by adding them as axioms then you could derive a contradiction in set theory without them. Gödel accomplished this by defining a certain minimal model of set theory, the constructible universe, and showing that in this model both axioms hold. Cohen then completed the proof of independence by showing that you can construct a model of set theory in which both axioms are false. To do so, he had to invent a new technique: forcing.

His Wikipedia biography has the oddest snippet:

His twin sons Steven and Eric played the Dancing Twins on the TV show Ally McBeal.

Is that really true?

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