Zobrazeno 1 - 10
of 340
pro vyhledávání: '"Krueger, John A."'
Autor:
Krueger, John
For any $2 \le n < \omega$, we introduce a forcing poset using generalized promises which adds a normal $n$-splitting subtree to a $(\ge \! n)$-splitting normal Aronszajn tree. Using this forcing poset, we prove several consistency results concerning
Externí odkaz:
http://arxiv.org/abs/2408.05380
For uncountable downwards closed subtrees $U$ and $W$ of an $\omega_1$-tree $T$, we say that $U$ and $W$ are strongly almost disjoint if their intersection is a finite union of countable chains. The tree $T$ is strongly non-saturated if there exists
Externí odkaz:
http://arxiv.org/abs/2406.10463
Autor:
Krueger, John, Stejskalova, Sarka
We introduce an abstract framework for forcing over a free Suslin tree with suborders of products of forcings which add some structure to the tree using countable approximations. The main ideas of this framework are consistency, separation, and the K
Externí odkaz:
http://arxiv.org/abs/2402.00226
We prove that the consistency strength of Martin's Maximum restricted to partial orders of cardinality $\omega_1$ follows from the consistency of ZFC.
Externí odkaz:
http://arxiv.org/abs/2307.06494
Autor:
Krueger, John
We analyze a countable support product of a free Suslin tree which turns it into a highly rigid Kurepa tree with no Aronszajn subtree.
Externí odkaz:
http://arxiv.org/abs/2303.05633
Autor:
Krueger, John
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 isomorphic. We also show that if $S$ is a free normal Suslin tree, then for
Externí odkaz:
http://arxiv.org/abs/2202.06144
Autor:
Krueger, John
We construct a large family of normal $\kappa$-complete $\mathbb{R}_\kappa$-embeddable non-special $\kappa^+$-Aronszajn trees which have no club isomorphic subtrees using an instance of the proxy principle of Brodsky-Rinot.
Externí odkaz:
http://arxiv.org/abs/2101.01814
Autor:
Krueger, John
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 orders to $\omega_1$-trees, and prove that an $\omega_1$-tree is entangled
Externí odkaz:
http://arxiv.org/abs/1910.08793
Autor:
Krueger, John
In this article we prove three main theorems: (1) guessing models are internally unbounded, (2) for any regular cardinal $\kappa \ge \omega_2$, $\textsf{ISP}(\kappa)$ implies that $\textsf{SCH}$ holds above $\kappa$, and (3) forcing posets which have
Externí odkaz:
http://arxiv.org/abs/1903.10476
Autor:
Gilton, Thomas, Krueger, John
Assuming the existence of a Mahlo cardinal, we construct a model in which there exists an $\omega_2$-Aronszajn tree, the $\omega_1$-approachability property fails, and every stationary subset of $\omega_2 \cap \mathrm{cof}(\omega)$ reflects.
Externí odkaz:
http://arxiv.org/abs/1901.02940