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Paper IPM / M / 16084  


Abstract:  
We discuss the generalized Kurepa hypothesis KH_{λ} at singular cardinals λ. In particular, we answer questions of Erdï¿½?sï¿½??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 settheoretic topology, NorthHolland, Amsterdam, pp. 235ï¿½??293, 1984, Israel J Math 52(1ï¿½??2): pp. 53ï¿½??58, 1985) by showing that GCH does not imply KH_{ℵω } nor the existence of a family F ⊆ [ℵ_{ω} ]^{ℵ0} of size ℵ_{ω+1} such that Open image in new window has size ℵ_{0} for every X ⊆ S, X=ℵ_{0}.
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