Related papers: Comparing the degrees of enumerability and the clo…
Existentially closed groups are, informally, groups that contain solutions to every consistent finite system of equations and inequations. They were introduced in 1951 in an algebraic context and subsequent research elucidated deep…
Given two closed oriented manifolds $M,N$ of the same dimension, we denote the set of degrees of maps from $M$ to $N$ by $D(M,N)$. The set $D(M,N)$ always contains zero. We show the following (non-)realisability results: (i) There exists an…
We extend some results on even sets of nodes which have been proved for surfaces up to degree 6 to surfaces up to degree 10. In particular, we give a formula for the minimal cardinality of a nonempty even set of nodes.
In this note we study associative dialgebras proving that the most interesting such structures arise precisely when the algebra is not semiprime. In fact the presence of some "perfection" property (simpleness, primitiveness, primeness or…
Tevelev degrees in Gromov-Witten theory are defined whenever there are virtually a finite number of genus $g$ maps of fixed complex structure in a given curve class $\beta$ through $n$ general points of a target variety $X$. These virtual…
We prove an inequality for the entropy numbers in terms of nonlinear Kolmogorov's widths. This inequality is in a spirit of known inequalities of this type and it is adjusted to the form convenient in applications for $m$-term…
Answering an open question raised by Cooper, we show that there exist $\Delta^0_2$ sets $D$ and $E$ such that the singleton degree of $E$ is a minimal cover of the singleton degree of $D$. This shows that the $\Sigma^{0}_{2}$ singleton…
We investigate the complexity of embeddings between bi-embeddable structures. In analogy with categoricity spectra, we define the bi-embeddable categoricity spectrum of a structure $\mathcal A$ as the family of Turing degrees that compute…
For oriented connected closed manifolds of the same dimension, there is a transitive relation: $M$ dominates $N$, or $M \ge N$, if there exists a continuous map of non-zero degree from $M$ onto $N$. Section 1 is a reminder on the notion of…
We propose a new definition of Koszulity for graded algebras where the degree zero part has finite global dimension, but is not necessarily semi-simple. The standard Koszul duality theorems hold in this setting. We give an application to…
Bidirected graphs generalize directed and undirected graphs in that edges are oriented locally at every node. The natural notion of the degree of a node that takes into account (local) orientations is that of net-degree. In this paper, we…
We investigate the computability-theoretic properties of valued fields, and in particular algebraically closed valued fields and $p$-adically closed valued fields. We give an effectiveness condition, related to Hensel's lemma, on a valued…
In this paper we study the existence of gradings on finite dimensional associative algebras. We prove that a connected algebra $A$ does not have a non-trivial grading if and only if $A$ is basic, its quiver has one vertex, and its group of…
We investigate big Ramsey degrees of finite substructures of the universal countable homogeneous meet-tree and its binary variant. We prove that structures containing antichains have infinite big Ramsey degrees, and the big Ramsey degree of…
Generalizing the notion of the degree of a finite-to-one factor code from a shift of finite type, the class degree of a possibly infinite-to-one factor extends many important properties of degree. In this paper, introducing class degree, we…
We explore the notion of degree of asymmetry for integer sequences and related combinatorial objects. The degree of asymmetry is a new combinatorial statistic that measures how far an object is from being symmetric. We define this notion…
For mass problems $P,Q\subseteq {\mathbb{N}^\mathbb{N}}$ (Baire space), $P$ is Medvedev reducible to $Q$ ($P\leq_sQ$) if for some Turing funcional $\Phi$, $\Phi(Q)\subseteq P$, and Medvedev equivalent to $Q$ if also $Q\leq_sP$. Shafer asked…
We show that for an endomorphism of an abelian variety defined over an algebraically closed field of arbitrary characteristic, the second cohomological dynamical degree coincides with the first numerical dynamical degree.
In this paper we consider big Ramsey degrees of finite chains in countable ordinals. We prove that a countable ordinal has finite big Ramsey degrees if and only if it is smaller than $\omega^\omega$. Big Ramsey degrees of finite chains in…
We introduce the point degree spectrum of a represented space as a substructure of the Medvedev degrees, which integrates the notion of Turing degrees, enumeration degrees, continuous degrees, and so on. The notion of point degree spectrum…