John Krueger

collaborators

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 Strong Kurepa Tree

John Krueger

We prove that it is consistent that there exists a Kurepa tree $T$ such that $^{I ¨ _{1}} 2$ is a continuous image of the topological space $[T]$ consisting of all cofinal branches of…

math.LO2025

Forcing Over a Free Suslin Tree

John Krueger, Sarka Stejskalova, Å Ã¡rka StejskalovÃ¡

We introduce a forcing for adding almost disjoint automorphisms of a normal infinitely splitting $I ¨ _{1}$ -tree $T$ with countable approximations. Assuming that $T$ is a free Suslin t…