Related papers: The singleton degrees of the $\Sigma^0_2$ sets are…
We show that for both the unary relation of transcendence and the finitary relation of algebraic independence on a field, the degree spectra of these relations may consist of any single computably enumerable Turing degree, or of those c.e.…
This note is the third part of our work devoted to uniqueness sets for spaces of entire functions. Given a discrete set $\Lambda$ with angular density $\Delta$ with respect to the order $\rho$, satisfying some regularity condition, we show…
In this paper, we give a new and efficient algebraic criterion for the pure as well as non-pure shellability of simplicial complex $\Delta$ over [n]. We also give an algebraic characterization of a leaf in a simplicial complex (defined in…
We construct a 2-category of differential graded schemes. The local affine models in this theory are differential graded algebras, which are graded commutative with unit over a field of characteristic zero, are concentrated in non-positive…
Singletons are those unitary irreducible modules of the Poincare or (anti) de Sitter group that can be lifted to unitary modules of the conformal group. Higher-spin algebras are the corresponding realizations of the universal enveloping…
We introduce a special class of supersingular curves over $\mathbb{F}_{p^2}$, characterized by the existence of non-integer endomorphisms of small degree. A number of properties of this set is proved. Most notably, we show that when this…
Illumination complexes are examples of 'flat polyhedral complexes' which arise if several copies of a convex polyhedron (convex body) Q are glued together along some of their common faces (closed convex subsets of their boundaries). A…
Let ${\cal E}$ be a topos, ${{\rm Dec}({\cal E}) \rightarrow {\cal E}}$ be the full subcategory of decidable objects, and ${{\cal E}_{\neg\neg} \rightarrow {\cal E}}$ be the full subcategory of double-negation sheaves. We give sufficient…
We classify strongly homotopy Lie algebras - also called L-infinity algebras - of one even and two odd dimensions, which are related to $2|1$-dimensional $Z_2$-graded Lie algebras. What makes this case interesting is that there are many…
We investigate what collections of c.e.\ Turing degrees can be realised as the collection of elements of a separating $\Pi^0_1$ class of c.e.\ degree. We show that for every c.e.\ degree $\mathbf{c}$, the collection $\{\mathbf{c},…
This paper investigates finiteness conditions for gentle and skew-gentle algebras. First, we prove that a skew-gentle algebra is $\tau$-tilting finite if and only if it is representation-finite, which extends the result for gentle algebras…
Richter, Stephan, and Zhang asked whether every nonrecursive many-one degree contains a least finite-one degree. We prove this for every nonrecursive \ce\ many-one degree containing a $D$-maximal set. The proof handles the simple cases via…
For a graph $G$, we denote by $\sigma_{2}(G)$ the minimum degree sum of two non-adjacent vertices if $G$ is non-complete; otherwise, $\sigma_{2}(G) = +\infty$. In this paper, we prove the following two results: (i) If $s_{1}, s_{2} \ge 2$…
We give upper bounds for the number of rational elliptic surfaces in some families having positive rank, obtaining in particular that these form a subset of density zero. This confirms Cowan's conjecture (arXiv:2009.08622v2) in the case…
We obtain several formulas for the Euclidean distance degree (ED degree) of an arbitrary nonsingular variety in projective space: in terms of Chern and Segre classes, Milnor classes, Chern-Schwartz-MacPherson classes, and an extremely…
An important theorem by Timofte states that nonnegativity of real $n$-variate symmetric polynomials of degree $d$ can be decided at test sets given by all points with at most $\lfloor\frac{d}{2}\rfloor$ distinct components. However, if the…
We study the limiting degree distribution of the vertex splitting model introduced in \cite{DDJS:2009}. This is a model of randomly growing ordered trees, where in each time step the tree is separated into two components by splitting a…
Let $\mathcal R$ be a $\Sigma^1_1$ binary relation and call a set $\mathcal R$-discrete iff no two distinct of its elements are $\mathcal R$-related. We show that in the extension of $\mathbf{L}$ by iterated Sacks forcing, there is a…
In this article, we prove some subsets of the set of natural numbers $\mathbb{N}$ and any non-zero ideals of an order of imaginary quadratic fields are fractionally dense in $\mathbb{R}_{>0}$ and $\mathbb{C}$ respectively.
In this note we show that a set is provably $\Delta^0_2$ in the fragment $I\Sigma_n$ of arithmetic iff it is $I\Sigma_n$-provably in the class $D_\alpha$ of $\alpha$-r.e. sets in the Ershov hierarchy for an $\alpha <_{\epsilon_0}…