the notion of generic in set theory

José Manuel Rodríguez Caballero josephcmac at
Fri Feb 14 20:20:48 EST 2020

Dear FOM members,
  Concerning the following statement taken from [1]:

if you take set theory and you do not allow generic then obviously the
> continuum hypothesis is true, but if you allow generic, then obviously it
> is not true.

I would like to ask the following questions:
1) What does it mean generic in this setting?
2) Is there a formal definition of generic?
3) Which option, between allowing and not allowing generic, does mainstream
mathematicians prefer concerning set theory?

Kind regards,
Jose M.


[1] What is a Manifold? - Mikhail Gromov (time 31:28 / 53:55)

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