5 citations · 7 across the 7 of their papers we have counts for
19 papers
On the Consistency Strength of MM()
Natasha Dobrinen, John Krueger, Pedro Marun +2
We prove that the consistency strength of Martin's Maximum restricted to partial orders of cardinality follows from the consistency of ZFC.
A Rigid Kurepa Tree From a Free Suslin Tree
John Krueger
We analyze a countable support product of a free Suslin tree which turns it into a highly rigid Kurepa tree with no Aronszajn subtree. In the process, we introduce a new rigidity p…
Suslin tree preservation and club isomorphisms
John Krueger
We construct a model of set theory in which there exists a Suslin tree and satisfies that any two normal Aronszajn trees, neither of which contains a Suslin subtree, are club isomo…
A Large Pairwise Far Family of Aronszajn Trees
John Krueger
We construct a large family of normal -complete -embeddable non-special -Aronszajn trees which have no club isomorphic subtrees using an instance of the proxy…
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…
The Harrington-Shelah Model with Large Continuum
Thomas Gilton, John Krueger
We prove from the existence of a Mahlo cardinal the consistency of the statement that holds and every stationary subset of reflects to an ordi…
Club isomorphisms on higher Aronszajn trees
John Krueger
We prove the consistency, assuming an ineffable cardinal, that any two normal countably closed -Aronszajn trees are club isomorphic. This work generalizes to higher cardinals…
Namba forcing, weak approximation, and guessing
Sean Cox, John Krueger
We prove a variation of Easton's lemma for strongly proper forcings, and use it to prove that, unlike the stronger principle , together with $2^ω\le ω…
The Approachability Ideal Without a Maximal Set
John Krueger
We develop a forcing poset with finite conditions which adds a partial square sequence on a given stationary set, with adequate sets of models as side conditions. We then develop a…
Indestructible Guessing Models and the Continuum
Sean Cox, John Krueger
We introduce a stronger version of an -guessing model, which we call an indestructibly -guessing model. The principle IGMP states that there are stationarily many indestr…
Mitchell's Theorem Revisited
Thomas Gilton, John Krueger
Mitchell's theorem on the approachability ideal states that it is consistent relative to a greatly Mahlo cardinal that there is no stationary subset of …
Coherent Adequate Sets and Forcing Square
John Krueger
We introduce the idea of a coherent adequate set of models, which can be used as side conditions in forcing. As an application we define a forcing poset which adds a square sequenc…
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…
Forcing with Adequate Sets of Models as Side Conditions
John Krueger
We present a general framework for forcing on with finite conditions using countable models as side conditions. This framework is based on a method of comparing countable mod…
Quotients of Strongly Proper Forcings and Guessing Models
Sean Cox, John Krueger
We prove that a wide class of strongly proper forcing posets have quotients with strong properties. Specifically, we prove that quotients of forcing posets which have simple univer…