John Krueger

collaborators

5 papers

math.LO2026

Countryman Lines and the Continuum Hypothesis

John Krueger, Eduardo Martinez Mendoza

We explore the prospect of basis-like results for the class of Aronszajn lines which are consistent with the Continuum Hypothesis (CH). In particular, we prove that each of the fol…

math.LO2026

Combinatorial Properties Related to the Higher Baumgartner's Axiom

John Krueger

We isolate two combinatorial properties, each expressible by a $I^_{2}$ -sentence over the structure $(H (I ¨ _{3}), \in, I ¨ _{1}, I ¨ _{2}, NS_{I ¨ _{2}})$ , such that each property is consistent…

math.LO2025

Some Results on Finitely Splitting Subtrees of Aronszajn Trees

John Krueger

For any $2 \leq n < I ¨ $ , we introduce a forcing poset using generalized promises which adds a normal $n$ -splitting subtree to a $(\geq n)$ -splitting normal Aronszajn tree. Using t…

math.LO2025

An almost Kurepa Suslin tree with strongly non-saturated square

John Krueger, Eduardo Martinez Mendoza

For uncountable downwards closed subtrees $U$ and $W$ of an $I ¨ _{1}$ -tree $T$ , we say that $U$ and $W$ are strongly almost disjoint if their intersection is a finite union of countab…

math.LO2025

A Strongly Non-Saturated Aronszajn Tree Without Weak Kurepa Trees

John Krueger, Å Ã¡rka StejskalovÃ¡

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…