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math.LO2025
A virtual five element basis for the uncountable linear orders
John Krueger, Justin Tatch Moore
We prove that for every Aronzsajn line A and every Countryman line C, there is a proper forcing extension in which A contains an isomorphic copy of either C or its converse C*. As…
math.LO2025
Ultrafilters over Successor Cardinals and the Tukey Order
Tom Benhamou, Justin T. Moore, Luke Serafin
We study ultrafilters on regular uncountable cardinals, with a primary focus on , and particularly in relation to the Tukey order on directed sets. Results include the indepen…