Related papers: On $\omega_3$-chains in P($\omega_1$) mod finite

We show that in the $\mathbb{P}_{\max}$ extension of a certain Chang-type model of determinacy, if $\kappa\in\{\omega_1, \omega_2, \omega_3\}$, then the restriction of the club filter on $\kappa\cap\mathrm{Cof}(\omega)$ to HOD is an…

In this work, we investigated the existence of compacton-like configuration in the O(3)-sigma model. We consider a minimally coupled O(3)-sigma model with a gauge field governed by a generalized Chern-Simons term. Contrary to that…

We reimplement the creature forcing construction used by Fischer et al. (arXiv:1402.0367) to separate Cicho\'{n}'s diagram into five cardinals as a countable support product. Using the fact that it is of countable support, we augment our…

We prove Iitaka's $C_{n,m}$ conjecture for $3$-folds over the algebraic closure of finite fields. Along the way we prove some results on the birational geometry of log surfaces over nonclosed fields and apply these to existence of relative…

Given a countable model of set theory, we study the structure of its generic multiverse, the collection of its forcing extensions and ground models, ordered by inclusion. Mostowski showed that any finite poset embeds into the generic…

We demonstrate that the number of cycles for two problems of the family of generalized 3x+1 mappings is possible finite.

We analyze the mock modular behavior of $\bar{P}_\omega(q)$, a partition function introduced by Andrews, Dixit, Schultz, and Yee. This function arose in a study of smallest parts functions related to classical third order mock theta…

Solovay's arithmetical completeness theorem states that the modal logic of provability coincides with the modal logic $\mathbf{GL}$. Hamkins and L\"owe studied the modal logical aspects of set theoretic multiverse and proved that the modal…

In the present paper we are interested in properties of forcing notions which measure in a sense the distance between the ground model reals and the reals in the extension. We look at the ways the ``new'' reals can be aproximated by ``old''…

We present a methodology that extends invariant manifold theory to a class of autonomous piecewise linear systems with nonsmoothness at the equilibrium, providing a framework for model order reduction in mechanical structures with compliant…

We give a new simple proof of the decidability of the First Order Theory of (omega^omega^i,+) and the Monadic Second Order Theory of (omega^i,<), improving the complexity in both cases. Our algorithm is based on tree automata and a new…

A connected 1-factorisation is a 1-factorisation of a hypergraph for which the union of each pair of distinct 1-factors is a connected hypergraph. A uniform 1-factorisation is a 1-factorisation of a hypergraph for which the union of each…

We present several $\mathsf{ZFC}$ examples of compactifications $\gamma\omega$ of $\omega$ such that their remainders $\gamma\omega\backslash\omega$ are nonseparable and carry strictly positive measures.

We exhibit a monotone function computable by a monotone circuit of quasipolynomial size such that any monotone circuit of polynomial depth requires exponential size. This is the first size-depth tradeoff result for monotone circuits in the…

The technique of symmetric extensions is derived from forcing and it is one of the most important tools for studying models without the Axiom of Choice. Despite being incredibly successful since the 1960s, our understanding of the technique…

A topological space $X$ is $\mathbb R^{\omega_1}$-factorizable if any continuous function $f\colon X\to \mathbb R^{\omega_1}$ factors through a continuous function from $X$ to a second-countable space. It is shown that a Tychonoff space $X$…

We introduce a variant of Martin's axiom, called the grounded Martin's axiom, which asserts that the universe is a ccc forcing extension in which Martin's axiom holds for posets in the ground model. This principle already implies several of…

A connected forcing set of a graph is a zero forcing set that induces a connected subgraph. In this paper, we introduce and study CF-dense graphs -- graphs in which every vertex belongs to some minimum connected forcing set. We identify…

We make use of a finite support product of the Jensen minimal $\varPi^1_2$ singleton forcing to define a model in which $\varPi^1_2$ Uniformization fails for a set with countable cross-sections. We also define appropriate submodels of the…

Assume $\text{MA}(\kappa)$. We show that for every real chain of size $\kappa$ in the quotient Boolean algebra $P(\omega)/fin$ we can find an almost chain of representatives such that every $n\in\omega$ oscillates at most three times along…