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A point in Baire space is found for which the first derived ωlimit set is not Borel, whilst the second is empty. A second point is found for which the sequence of derived ω-limit sets does not stabilise until the first uncountable ordinal. The two points are recursive. 2 A. R. D. MATHIASdoi:10.1017/s0305004104008254 fatcat:ch2mxbh65feffl4iyxcoky4oli