8
$\begingroup$

What is a good source for Silver's proof (or a more modern version) that Con($\exists \omega_1$-Erdos cardinal) implies Con(Chang's Conjecture)?

Silver's original proof seems to have never been published and I didn't find a proof in the set theory books I looked at (i.e. Jech's "Set Theory: the 3rd Millennium Edition" and Kanamori's "Higher Infinite")

$\endgroup$

2 Answers 2

7
$\begingroup$

Some references:

1) K. Kunen, Saturated ideals: The consistency of $(\omega_{n+2}, \omega_{n+1})\twoheadrightarrow (\omega_{n+1}, \omega_n)$ for $n \geq 1$ has been established starting with a huge cardinal.

2) H.-D. Donder and J.-P. Levinski, Some principles related to Chang's Conjecture: A proof is given without use of Martin's Axiom, and also using a Levy collapse instead of a Silver collapse.

3) K. Devlin, A note on a problem of Erdos and Hajnal: A generalization of Silver's theorem is proved.

$\endgroup$
6
$\begingroup$

A sketch of Silver's original argument appears in section 19 here: http://math.bu.edu/people/aki/e.pdf

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.