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MR2470843 (2009k:03087) 03E55 (03E40) Hamkins, Joel David; Johnstone, Thomas A. The proper and semi-proper forcing axioms for forcing notions that preserve $\aleph\sb 2$$\aleph\sb 2$ or $\aleph\sb 3$$\aleph\sb 3$. Proc. Amer. Math. Soc. 137 (2009), no. 5, 1823–1833.

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