Related papers: Almost Souslin Kurepa trees

An inaccessible cardinal kappa is supercompact when (kappa, lambda)-ITP holds for all lambda greater than or equal to kappa. We prove that if there is a model of ZFC with infinitely many supercompact cardinals, then there is a model of ZFC…

We determine when two almost automorphisms of a regular tree are conjugate. This is done by combining the classification of conjugacy classes in the automorphism group of a level-homogeneous tree by Gawron, Nekrashevych and Sushchansky and…

We investigate questions involving Aronszajn trees, square principles, and stationary reflection. We first consider two strengthenings of $\square(\kappa)$ introduced by Brodsky and Rinot for the purpose of constructing $\kappa$-Souslin…

The well known bunkbed conjecture about percolation on finite graphs is now resolved; Gladkov, Pak and Zimin, building upon work of Hollom, have constructed a counterexample. We revisit this conjecture and study it in the broader context of…

We study filtration of quasi--coherent sheaves. We prove a version of Kaplansky Theorem for quasi--coherent sheaves, by using Drinfeld's notion of almost projective module and the Hill Lemma. We also show a Lazard-like theorem for flat…

We prove that for any semi-Dirichlet form $(\epsilon, D(\epsilon))$ on a measurable Lusin space $E$ there exists a Lusin topology with the given $\sigma$-algebra as the Borel $\sigma$-algebra so that $(\epsilon, D(\epsilon))$ becomes…

We show that any compact, connected set $K$ in the plane can be approximated by the critical points of a polynomial with two critical values. Equivalently, $K$ can be approximated in the Hausdorff metric by a true tree in the sense of…

Let $(G,g)$ be a 4-dimensional Riemannian Lie group with a 2-dimensional left-invariant, conformal foliation $\F$ with minimal leaves. Let $J$ be an almost Hermitian structure on $G$ adapted to the foliation $\F$. We classify such…

We prove the exponential growth of the cardinality of the set of numbers of spanning trees in simple (and planar) graphs on $n$ vertices, answering a question of Sedl\'a\v{c}ek from 1969. The proof uses a connection with continued…

We prove that every oriented tree on $n$ vertices with bounded maximum degree appears as a spanning subdigraph of every directed graph on $n$ vertices with minimum semidegree at least $n/2+o(n)$. This can be seen as a directed graph…

We prove the rather counterintuitive result that there exist finite transitive graphs H and integers k such that the Free Uniform Spanning Forest in the direct product of the k-regular tree and H has infinitely many trees almost surely.…

We show that, consistently, there can be maximal subtrees of P (omega) and P (omega) / fin of arbitrary regular uncountable size below the size of the continuum. We also show that there are no maximal subtrees of P (omega) / fin with…

By work of a number of authors, beginning with Scott and culminating with Galashin and Lam, the coordinate rings of positroid varieties in the Grassmannian carry cluster algebra structures. In fact, they typically carry many such…

A well-known theorem of Nash-Williams shows that the collection of locally finite trees under the topological minor relation results in a BQO. Set theoretically, two very natural questions arise: (1) What is the number $\lambda$ of…

In this paper we study the quasi-forest simplicial complexes and we define the concept of simplicial $k$-cycle (denoted by $\mathcal{S}_k$) and simplicial $k$-point (denoted by $\mathcal{P}_k$). We show that a simplicial complex $\Delta$ is…

We investigate two variants of splitting tree forcing, their ideals and regularity properties. We prove connections with other well-known notions, such as Lebesgue measurablility, Baire- and Doughnut-property and the Marczewski field.…

In this paper, we provide some topological criteria for the Poisson Dixmier-Moeglin equivalence for $A$ in terms of the poset $({\rm P. spec A}, \subseteq)$ and the symplectic leaf or core stratification on its maximal spectrum. In…

Let $R$ be a complete discrete valuation ring of equal characteristic $p>0$. Given a $\mathbb{Z}/p$-Galois cover of a formal disc over $R$, one can derive from it a semi-stable model for which the specializations of branch points are…

We prove via a composition lemma, the Kotzig-Ringel-Rosa conjecture, better known as the Graceful Labeling Conjecture. We also prove via a stronger version of the composition lemma a stronger form of the Graceful Labeling Conjecture.

The Halpern-L\"auchli theorem, a combinatorial result about trees, admits an elegant proof due to Harrington using ideas from forcing. In an attempt to distill the combinatorial essence of this proof, we isolate various partition principles…