[FOM] Cohen and Kunen as sources on forcing
Colin McLarty
colin.mclarty at case.edu
Sat May 19 09:47:18 EDT 2007
My thanks to everyone for answers to my earlier query. Now I have a
student who wants an independent study on set theory. He's a math
major and has taken the course proving the (first) Gödel incompleteness
theorem, but has no axiomatic set theory.
I have twice gotten through the basic forcing model construction: first
from Cohen's SET THEORY AND THE CONTINUUM HYPOTHESIS, and later from
Kunen SET THEORY. But sadly I have never gone on to learn any specific
forcing proof. Now is my chance.
So I'd like advice on Cohen versus Kunen. I understand that to become
a research set theorist the student would need Kunen. Is Cohen a
better beginner's book?
Kunen centers his account on Martin's axiom which gives a great view of
*why* forcing works -- but until you have some idea of what forcing is,
MA looks bizarre.
Kunen's account is much longer than Cohen's and will appear rather dry
and technical to an undergrad who as of now barely knows what well-
founding is. I.e. he may know the definition but does not know the
idea.
Cohen gives a nicer general introduction for mathematicians to
axiomatic set theory. Kunen assumes you know more to begin with.
Cohen is the creator of the idea, and his work is a historic document.
So: would it be terribly unfair to use Cohen? Would I cheat the
student of the benefit of later improvements? Or does Cohen give a
still-usable introduction to the basics?
Amazon.com believes that both Cohen and Kunen are out of print. Jech
SET THEORY is in print, and I'm sure that like Kunen it is a fine book
for a resarch set theorist, but it puts an awful lot of detail on
descriptive set theory before even the inner model proof of consistency
of V=L. It does not seem right for an introduction to axiomatic set
theory.
best, Colin
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