Geodesic
Reflection implies the SCH
Saharon Shelah1
1 Institute of Mathematics The Hebrew University Jerusalem, Israel and Mathematics Department Rutgers University New Brunswick, NJ 08854, U.S.A.
Fundamenta Mathematicae, Tome 198 (2008) no. 2, pp. 95-111

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We prove that, e.g., if $\mu > \mathop{\rm cf}\nolimits(\mu) = \aleph_0$ and $\mu > 2^{\aleph_0}$ and every stationary family of countable subsets of $\mu^+$ reflects in some subset of $\mu^+$ of cardinality $\aleph_1$, then the SCH for $\mu^+$ holds (moreover, for $\mu^+$, any scale for $\mu^+$ has a bad stationary set of cofinality $\aleph_1$). This answers a question of Foreman and Todorčević who get such a conclusion from the simultaneous reflection of four stationary sets.
DOI : 10.4064/fm198-2-1
Keywords: prove mathop nolimits aleph aleph every stationary family countable subsets reflects subset cardinality aleph sch holds moreover scale has bad stationary set cofinality nbsp aleph answers question foreman todor evi who get conclusion simultaneous reflection stationary sets

Saharon Shelah 1

1 Institute of Mathematics The Hebrew University Jerusalem, Israel and Mathematics Department Rutgers University New Brunswick, NJ 08854, U.S.A. 
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Saharon Shelah. Reflection implies the SCH. Fundamenta Mathematicae, Tome 198 (2008) no. 2, pp. 95-111. doi: 10.4064/fm198-2-1

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