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| Paper IPM / M / 16084 |
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| Abstract: | |
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We discuss the generalized Kurepa hypothesis KHλ at singular cardinals λ. In particular, we answer questions of Erd�?s�??Hajnal (in: Proceedings of the Symposium Pure Mathematics, Part I, University of California, Los Angeles, CA, 1967) and Todorcevic (Trees and linearly ordered sets. Handbook of set-theoretic topology, North-Holland, Amsterdam, pp. 235�??293, 1984, Israel J Math 52(1�??2): pp. 53�??58, 1985) by showing that GCH does not imply KHℵω nor the existence of a family F ⊆ [ℵω ]ℵ0 of size ℵω+1 such that Open image in new window has size ℵ0 for every X ⊆ S, |X|=ℵ0.
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