5 papers
Entangledness in Suslin lines and trees
John Krueger
We introduce the idea of a weakly entangled linear order, and show that it is consistent for a Suslin line to be weakly entangled. We generalize the notion of entangled linear orde…
Guessing models imply the singular cardinal hypothesis
John Krueger
In this article we prove three main theorems: (1) guessing models are internally unbounded, (2) for any regular cardinal , implies that h…
A note on the eightfold way
Thomas Gilton, John Krueger
Assuming the existence of a Mahlo cardinal, we construct a model in which there exists an -Aronszajn tree, the -approachability property fails, and every stationary subse…
Parametrized Measuring and Club Guessing
David Aspero, John Krueger
We introduce Strong Measuring, a maximal strengthening of J. T. Moore's Measuring principle, which asserts that every collection of fewer than continuum many closed bounded subsets…
A forcing axiom for a non-special Aronszajn tree
John Krueger
Suppose that is an -Aronszajn tree with no stationary antichain. We introduce a forcing axiom PFA() for proper forcings which preserve these properties of . We…