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  1. How High Can Baumgartner’s $${\Mathcal{I}}$$ I -Ultrafilters Lie in the P-Hierarchy?Michał Machura & Andrzej Starosolski - 2015 - Archive for Mathematical Logic 54 (5-6):555-569.
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  • Cascades, Order, and Ultrafilters.Andrzej Starosolski - 2014 - Annals of Pure and Applied Logic 165 (10):1626-1638.
    We investigate mutual behavior of cascades, contours of which are contained in a fixed ultrafilter. This allows us to prove that the class of strict JωωJωω-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+1Jωω+1-ultrafilter.
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