In the 80s, Foreman showed the consistency of (aleph_{n+1},aleph_n) —>> (aleph_{m+1},aleph_m) holding simultaneously for all natural numbers n > m, starting from a 2-huge cardinal. He asked whether a global version of Chang’s conjecture is consistent. We answer this, showing that it is consistent from the same hypothesis that for all pairs of regular cardinals mu < kappa, (kappa^+,kappa) —>> (mu^+,mu). The method uses a relatively simple forcing iteration, and it answers some technical questions raised by Shioya. We also discuss some related issues about singular cardinals.
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