Related papers: Almost Souslin Kurepa trees

We show that there are proper forcings based upon countable trees of creatures that specialize a given Aronszajn tree.

In a previous article by two of the present authors and S. Bonzio, \L ukasiewicz near semirings were introduced and it was proven that basic algebras can be represented (precisely, are term equivalent to) as near semirings. In the same work…

We show that compact cardinals and {\rm MM} are sensitive to $\lambda$-closed forcings for arbitrarily large $\lambda$. This is done by adding 'regressive' $\lambda$-Kurepa-trees in either case. We argue that the destruction of regressive…

The strength of an extension of Kruskal's Theorem to certain pairs of cohabitation trees is calibrated.

For any cardinal $\kappa \geq 2$, there is a unique complete real tree whose points all have valence $\kappa$. In this note, we show that, when $\kappa \geq 3$, it is necessary to assume completeness. More precisely, we show that there…

In this note, we establish the hardness of approximation of the problem of computing the minimal size of a $\delta$-sufficient reason for decision trees.

Define (*) There exists $(\phi_n:\omega_1\to \omega_1:n<\omega)$ such that for every uncountable $I$ which is a subset of $\omega_1$ there exists $n$ such that $\phi_n$ maps $I$ onto $\omega_1$. This is roughly what Sierpinski in his book…

We prove that for every Aronzsajn line A and every Countryman line C, there is a proper forcing extension in which A contains an isomorphic copy of either C or its converse C*. As a corollary, we obtain answers to several related questions…

Suppose that there's no transitive model of ZFC + there's a strong cardinal, and let K denote the core model. It is shown that if \delta has the tree property then \delta^{+K} = \delta^+ and \delta is weakly compact in K.

We show that if CH holds and either (i) there exists an $\omega_1$-Kurepa tree, or (ii) $\square(\omega_2)$ holds, then there are regular $T_1$ Lindel\"of spaces $X_0$ and $X_1$ with points $G_\delta$ such that $e(X_0 \times X_1)>2^\omega$.

In this note, we show that locally finite quasi-transitive graphs are quasi-isometric to trees if and only if every other locally finite quasi-transitive graph quasi-isometric to them is minor excluded. This generalizes results by…

We show that it is consistent, relative to $\omega$ many supercompact cardinals, that the super tree property holds at $\aleph_n$ for all $2 \leq n < \omega$ but there are weak square and a very good scale at $\aleph_{\omega}$.

Since being isolated by Viale and Weiss in 2009, the Guessing Model Property has emerged as a particularly prominent and powerful consequence of the Proper Forcing Axiom. In this paper, we investigate connections between variations of the…

We introduce a method of constructing a forcing along a simplified $(\kappa,1)$-morass such that the forcing satisfies the $\kappa$-chain condition. Alternatively, this may be seen as a method to thin out a larger forcing to get a chain…

We discuss the Arhangel'skii-Tall problem and related questions in models obtained by forcing with a coherent Souslin tree.

Two-dimensional version of the classical Mycielski theorem says that for every comeager or conull set $X\subseteq [0,1]^2$ there exists a perfect set $P\subseteq [0,1]$ such that $P\times P\subseteq X\cup \Delta$. We consider…

This paper investigates some properties of the number of subtrees of a tree with given degree sequence. These results are used to characterize trees with the given degree sequence that have the largest number of subtrees, which generalizes…

We address ZFC inequalities between some cardinal invariants of the continuum, which turned to be true in spite of strong expectations given by [RoSh:470].

In this note we introduce the concept of a quasi-finite complex. Next, we show that for a given countable and locally finite CW complex L the following conditions are equivalent: (i) L is quasi-finite. (ii) There exists a [L]-invertible…

We present S. Todorcevic's method of forcing with a coherent Souslin tree over restricted iteration axioms as a black box usable by those who wish to avoid its complexities but still access its power.