3 papers
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
A Strongly Non-Saturated Aronszajn Tree Without Weak Kurepa Trees
John Krueger, Šárka Stejskalová
Assuming the negation of Chang's conjecture, there is a c.c.c. forcing which adds a strongly non-saturated Aronszajn tree. Using a Mahlo cardinal, we construct a model in which the…
math.LO2014
Coherent Adequate Forcing and Preserving CH
John Krueger, Miguel Angel Mota
We develop a general framework for forcing with coherent adequate sets on as side conditions, where is a cardinal of uncountable cofinality. We describe a class o…