Related papers: Lattice initial segments of the Turing degrees

We classify 1-tilting classes over an arbitrary commutative ring. As a consequence, we classify all resolving subcategories of finitely presented modules of projective dimension at most 1. Both these collections are in 1-1 correspondence…

We survey theory developed over the past 10 years of semirings which need not be additively cancellative. The main feature is a specified ``null ideal'' $\mcA_0$ of a semiring $\mcA,$ taking the place of a zero element, which permits…

A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…

Crisp and lattice-valued ambiguous representations of one continuous semilattice in another one are introduced and operation of taking pseudo-inverse of the above relations is defined. It is shown that continuous semilattices and their…

Finitary/static semantics in the form of intersection type assignments have become a paradigm for analysing the fine structure of all sorts of lambda-models. The key step is the construction of a filter model isomorphic to a given…

In this paper we investigate the class of rigid monomial ideals. We give a characterization of the minimal free resolutions of certain classes of these ideals. Specifically, we show that the ideals in a particular subclass of rigid monomial…

Diagonal groups are one of the classes of finite primitive permutation groups occurring in the conclusion of the O'Nan-Scott theorem. Several of the other classes have been described as the automorphism groups of geometric or combinatorial…

Let $k$ be a field of characteristic not two or three. We classify up to isomorphism all finite-dimensional Lie superalgebras $\mathfrak{g}=\mathfrak{g}_0\oplus \mathfrak{g}_1$ over $k$, where $\mathfrak{g}_0$ is a three-dimensional simple…

Let $\Gamma^{(x_0)}$ be a finite rooted tree, for which $\Gamma$ is the underlying tree and $x_0$ the root. Let $T$ be the Terwilliger algebra of $\Gamma$ with respect to $x_0$. We study the structure of the principal $T$-module. As a…

Toric geometry provides a bridge between the theory of polytopes and algebraic geometry: one can associate to each lattice polytope a polarized toric variety. In this paper we explore this correspondence to classify smooth lattice polytopes…

$\SOL$ geometry is one of the eight homogeneous Thurston 3-geomet-ri-es $$\EUC, \SPH, \HYP, \SXR, \HXR, \SLR, \NIL, \SOL.$$ In \cite{Sz10} the {\it densest lattice-like translation ball packings} to a type (type {\bf I/1} in this paper) of…

Let $k$ be a perfect field of characteristic $p \geq 3$, and let $K$ be a finite totally ramified extension of $K_0 = W(k)[p^{-1}]$. Let $L_0$ be a complete discrete valuation field over $K_0$ whose residue field has a finite $p$-basis, and…

Automatic structures are finitely presented structures where the universe and all relations can be recognized by finite automata. It is known that the isomorphism problem for automatic structures is complete for $\Sigma^1_1$; the first…

It is, by now, classical that lattices in higher rank semisimple groups have various rigidity properties. In this work, we add another such rigidity property to the list: uniform stability with respect to the family of unitary operators on…

The degree of a projective subscheme has an upper bound in term of the codimension and the reduction number. If a projective variety has an almost maximal degree, that is, the degree equals to the upper bound minus one, then its Betti table…

We construct a class of lattices in three and higher dimensions for which the number of dimer coverings can be determined exactly using elementary arguments. These lattices are a generalization of the two-dimensional kagome lattice, and the…

Let $X$ be a complete simplicial toric variety over a finite field $\mathbb{F}_q$ with homogeneous coordinate ring $S=\mathbb{F}_q[x_1,\dots,x_r]$ and split torus $T_X\cong (\mathbb{F}^*_q)^n$. We prove that vanishing ideal of a subset $Y$…

The degree spectrum of a countable structure is the set of all Turing degrees of presentations of that structure. We show that every nonlow Turing degree lies in the spectrum of some differentially closed field (of characteristic 0, with a…

In this paper, we completely classify the isomorphism classes of certain lattices $L_A(C)$ and $L_B(C)$ from a self-orthogonal code $C$ over the finite field $\mathbb{F}_p$, where $p$ is an odd prime. These lattices are obtained by…

We construct the minimal resolutions of three classes of monomial ideals: dominant, 1-semidominant, and 2-semidominant ideals. The families of dominant and 1-semidominant ideals extend those of complete and almost complete intersections. We…