Related papers: A Survey of Muchnik and Medvedev degrees

For $p \in [0,1]$ let $\mathcal D(p)$ be the mass problem of infinite bit sequences~$y$ (i.e., $\{0,1\}$-valued functions) such that for each computable bit sequence $x$, the bit sequence $ x \leftrightarrow y$ has asymptotic lower density…

In this expository article, we give a self-contained introduction to the wonderfully well-behaved class of pseudocompact algebras, focusing on the foundational classes of semisimple and separable algebras. We give characterizations of such…

Let ${\mathscr M}(p)$ $(p=2,3,\ldots)$ be the singlet vertex operator algebra and $\omega$ its conformal vector. We classify the simple weak ${\mathscr M}(p)$-modules with a non-zero element $u$ such that for some integer $s\geq 2$,…

For every prime $p$ and integer $n\ge 3$ we explicitly construct an abelian variety $A/\F_{p^n}$ of dimension $n$ such that for a suitable prime $l$ the group of quasi-isogenies of $A/\F_{p^n}$ of $l$-power degree is canonically a dense…

We characterize all profinite MV-algebras, these are MV-algebras that are inverse limits of finite MV-algebras. It is shown that these are exactly direct product of finite \L ukasiewicz's chains. We also prove that the category $\mathbb{M}$…

By using ergodic theoretic techniques following Hillel F\"{u}rstenberg, we prove that measurable subsets of a locally compact abelian group of positive upper density contain Szemer\'{e}di-wise configurations defined by an arbitrary compact…

Let $C$ be a nonsingular irreducible projective curve of genus $g\ge2$ defined over the complex numbers. Suppose that $1\le n'\le n-1$ and $n'd-nd'=n'(n-n')(g-1)$. It is known that, for the general vector bundle $E$ of rank $n$ and degree…

We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…

Let $G=(V(G),E(G))$ be a graph with set of vertices $V(G)$ and set of edges $E(G)$. A subset $S$ of $E(G)$ is called a $k$-nearly independent edge subsets if there are exactly $k$ pairs of elements of $S$ that share a common end. $Z_k(G)$…

We show that the Hrushovski-\fraisse limit of certain classes of trees lead to strictly superstable theories of various U-ranks. In fact, for each $ \alpha\in\omega+1\backslash\{0\} $ we introduce a strictly superstable theory of U-rank $…

We prove duality theorems for twisted Reidemeister torsions and twisted Alexander polynomials generalizing the results of Turaev. As a corollary we determine the parity of the degrees of twisted Alexander polynomials of 3-manifolds in many…

This paper is devoted to give a complete unified study of several weak forms of $\ddb-$Lemma on compact complex manifolds.

Subspace varieties are algebraic varieties whose elements are tensors with bounded multilinear rank. In this paper, we compute their degrees by computing their volumes.

We develop a theory of \emph{sharp measure zero} sets that parallels Borel's \emph{strong measure zero}, and prove a theorem analogous to Galvin-Myscielski-Solovay Theorem, namely that a set of reals has sharp measure zero if and only if it…

We examine sets of codes such that certain properties are invariant under the choice of oracle from a range of possible oracles and establish a connection between such codes and Medvedev reductions. In examing the complexity of such sets of…

We establish and fully characterize the multidimensional extension of the Stronger Central Sets Theorem. Additionally, we develop a polynomial generalization of this result. Our approach utilizes tools from the Algebra of the Stone-\v{C}ech…

We investigate the initial segments of the Medvedev lattice as Brouwer algebras, and study the propositional logics connected to them.

We begin to study the structure of Leibniz algebras having maximal cyclic subalgebras

This paper deals with new continuous and compact embedding theorems for the fractional Musielak-Sobolev spaces in $\mathbb{R}^d$. As an application, using the variational methods, we obtain the existence of nontrivial weak solution for the…

This is the second of two works concerning the Sobolev calculus on metric measure spaces and its applications. In this work, we focus on several approaches to vector calculus in the non-smooth setting of complete and separable metric spaces…