Cascades,order, and ultrafilters |
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Authors: | Andrzej Starosolski |
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Institution: | Silesian University of Technology, Faculty of Applied Mathematics, ul. Kaszubska 23, 44-101 Gliwice, Poland |
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Abstract: | We investigate mutual behavior of cascades, contours of which are contained in a fixed ultrafilter. This allows us to prove (ZFC) that the class of strict Jωω-ultrafilters, introduced by J.E. Baumgartner in 2], is empty. We translate the result to the language of <∞-sequences under an ultrafilter, investigated by C. Laflamme in 17], and we show that if there is an arbitrary long finite <∞-sequence under u, then u is at least a strict Jωω+1-ultrafilter. |
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Keywords: | 03E04 03E05 03E20 54A99 |
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