Related papers: PFA(S)[S] and the Arhangel'skii-Tall problem

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…

It is shown that the problem of computing the Strahler number of a binary tree given as a term is complete for the circuit complexity class uniform $\mathsf{NC}^1$. For several variants, where the binary tree is given by a pointer structure…

Motivated by a question from a recent paper by Gilton, Levine and Stejskalova, we obtain a new characterization of the ideal $J[\kappa]$, from which we confirm that $\kappa$-Souslin trees exist in various models of interest. As a corollary…

We show that for a Suslin ccc forcing notion $\mathbb Q$ adding a Hechler real, ``$\text{ZF}+\text{DC}_{\omega_1}+$all sets of reals are $I_{\mathbb Q,\aleph_0}$-measurable'' implies the existence of an inner model with a measurable…

We develop a toolbox for forcing over arbitrary models of set theory without the axiom of choice. In particular, we introduce a variant of the countable chain condition and prove an iteration theorem that applies to many classical forcings…

We study the computational complexity of graph planarization via edge contraction. The problem CONTRACT asks whether there exists a set $S$ of at most $k$ edges that when contracted produces a planar graph. We work with a more general…

A simple algebraic technique is developed to obtain deformed energy spectra for the P\"oschl-Teller potentials.

We consider the creation conditions of diverse hierarchical trees both analytically and numerically. A connection between the probabilities to create hierarchical levels and the probability to associate these levels into a united structure…

We develop some basic results about full amalgamation classes with intrinsic trascendentals. These classes have generics whose models may have finite subsets whose intrinsic closure is not contained in its algebraic closure. We will show…

We investigate the unbalanced ordinary partition relations of the form $\lambda \rightarrow {(\lambda, \alpha)}^{2}$ for various values of the cardinal $\lambda$ and the ordinal $\alpha$. For example, we show that for every infinite…

We determine the sharp constants for the fractional Sobolev inequalities associated with the conformally invariant fractional powers $\mathcal{L}_{s}(0<s<1)$ of the sublaplacian on H-type groups. From these inequalities we derive a sharp…

In this paper, we answer a question asked in "A minimal Prikry type forcing for singularizing a measurable cardinal" regarding a Mathias criteria for Tree-Prikry forcing. Also we will investigate Prikry forcing using various filters. For…

We derive a forcing axiom from the conjunction of square and diamond, and present a few applications, primary among them being the existence of super-Souslin trees. It follows that for every uncountable cardinal $\lambda$, if $\lambda^{++}$…

We consider the following basic problem in phylogenetic tree construction. Let $\mathcal{P} = \{T_1, \ldots, T_k\}$ be a collection of rooted phylogenetic trees over various subsets of a set of species. The tree compatibility problem asks…

In this article, we show that $\alpha$-fractal functions defined on Sierpi\'nski gasket (denoted by $\triangle$) depend continuously on the parameters involved in the construction. In the latter part of this article, the continuous…

For a given shape $S$ in the plane, one can ask what is the lowest possible density of a point set $P$ that pierces ("intersects", "hits") all translates of $S$. This is equivalent to determining the covering density of $S$ and as such is…

Safety-critical infrastructures must operate in a safe and reliable way. Fault tree analysis is a widespread method used for risk assessment of these systems: fault trees (FTs) are required by, e.g., the Federal Aviation Administration and…

We consider planar first-passage percolation and show that the time constant can be bounded by multiples of the first and second tertiles of the weight distribution. As a consequence we obtain a counter-example to a problem proposed by Alm…

Suppose that $T^*$ is an $\omega_1$-Aronszajn tree with no stationary antichain. We introduce a forcing axiom PFA($T^*$) for proper forcings which preserve these properties of $T^*$. We prove that PFA($T^*$) implies many of the strong…

This work addresses an enumeration problem on weighted bi-colored plane trees with prescribed vertex data, with all vertices labeled distinctly. We give a bijection proof of the enumeration formula originally due to Kochetkov, hence…