相关论文: Club does not imply the existence of a Suslin tree

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…

Various versions of club are shown to be different. A question of Soukup, Fuchino and Juhasz, is it consistent to have a stick without club, is answered as a consequence. The more detailed version of the paper, which is coming up, also…

We prove the consistency, assuming an ineffable cardinal, that any two normal countably closed $\omega_2$-Aronszajn trees are club isomorphic. This work generalizes to higher cardinals the property of Abraham-Shelah that any two normal…

In this note we answer a question of Kunen (15.13 [Mi91]) showing that it is consistent that there are full Souslin trees

We show it is consistent that there is a Souslin tree $S$ such that after forcing with $S$, $S$ is Kurepa and for all clubs $C \subset \omega_1$, $S\upharpoonright C$ is rigid. This answers Fuchs's questions in Club degrees of rigidity and…

We show that many countable support iterations of proper forcings preserve Souslin trees. We establish sufficient conditions in terms of games and we draw connections to other preservation properties. We present a proof of preservation…

We show that the existence of an almost Souslin Kurepa tree is consistent with $ZFC$. We also prove their existence in $L$. These results answer two questions from Zakrzewski.

We introduce a new combinatorial principle which we call $\clubsuit_{AD}$. This principle asserts the existence of a certain multi-ladder system with guessing and almost-disjointness features, and is shown to be sufficient for carrying out…

We will show it is consistent with $GCH$ that there is a minimal Kurepa tree with respect to club embeddings.

We show that the existence of a Suslin tree does not necessarily imply that there are uncountable minimal linear orders other than $\omega_1$ and $-\omega_1$, answering a question of J. Baumgartner. This is done by a Jensen-type iteration,…

We present a weak sufficient condition for the existence of Souslin trees at successor of regular cardinals. The result is optimal and simultaneously improves an old theorem of Gregory and a more recent theorem of the author.

We prove that mu = mu^{< mu}, 2^mu = mu^+ and ``there is a non reflecting stationary subset of mu^+ composed of ordinals of cofinality < mu'' imply that there is a mu-complete Souslin tree on mu^+ .

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…

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,…

We show if we use countable support iteration of forcing notions not adding reals that satisfy additional conditions, then the limit forcing does not add reals. As a result we prove that we can amalgamate two earlier methods and prove the…

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 property for trees, which says roughly speaking that any…

It is consistent that there exists a Souslin tree $T$ such that after forcing with it, $T$ becomes an almost Souslin Kurepa tree. This answers a question of Zakrzewski.

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…

We give a direct proof of the Cotlar-Stein lemma, which does not rely on the power trick.

We consider a transitive relation on the power set of $\omega_1$ and show if there is a maximal element with respect to this relation then there is a Kurepa tree with no Aronszajn subtree. We also show that if there is a maximal subset of…