[FOM] Continuum Hypothesis

Adrian-Richard-David Mathias Adrian-Richard-David.Mathias at univ-reunion.fr
Fri May 16 02:45:40 EDT 2003

A good start would be the two articles by W. Hugh Woodin in the 
Notices of the American Mathematical Society; the first was in 
the June/July issue, 2001, (Volume 48 number 6) pp567--576; the second in
the August issue of that year (Volume 48 number 7) pp 681-690. 

A lot has happened since Cohen. In the 60s it seemed that there would be
little to choose between different possible values, amongst the alephs, of
the continuum; but in the light of work starting in the 80s, it seems that 
the three contexts that permit the richest structure to the continuum are 

1) the continuum well-ordered and of size aleph_1

2) the continuum well-ordered and of size aleph_2

3) some version of the axiom of determinacy true and the continuum 
therefore not well-orderable. 

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