Related papers: Pure $\Sigma_2$-Elementarity beyond the Core
By the famous ADE classification rational double points are simple. Rational triple points are also simple. We conjecture that the simple normal surface singularities are exactly those rational singularities, whose resolution graph can be…
This article explores \Z_2-graded L_\infinity algebra structures on a 2|1-dimensional vector space. The reader should note that our convention on the parities is the opposite of the usual one, because we define our structures on the…
We extend the theory (formal part only} of algebras with one binary operation (our paper arXiv:math/0110333v1 [math.RA] 31 Oct 2001) to algebras with several operations of any arity.
Given a 2-category $\mathcal{A}$, a $2$-functor $\mathcal{A} \overset {F} {\longrightarrow} \mathcal{C}at$ and a distinguished 1-subcategory $\Sigma \subset \mathcal{A}$ containing all the objects, a $\sigma$-cone for $F$ (with respect to…
In this note, we use elementary submodels to prove that a separable monotonically normal compactum can be mapped on a separable metric space via a continuous function whose fibers have cardinality at most 2.
We present an algebraic structure in modules over integer rings with cardinality prime powers, which allows to define bases. With such structure, we prove a similar version for the basis extension theorem of linear algebra over fields.…
We present algorithms to classify isolated hypersurface singularities over the real numbers according to the classification by V.I. Arnold (Arnold et al., 1985). This first part covers the splitting lemma and the simple singularities; a…
An odd-odd nucleus is treated as the core-particle-hole system. The core is described by the Bohr Hamiltonian. Different collective potentials of the core are investigated. The odd particle and hole are assumed to be in the symmetric…
We determine the semisimplicity criterion for even partition algebras over the complex field. Specifically we prove that the even/2-tonal partition algebras $P_n^2(\delta)$ over $\mathbb{C}$ are semisimple for all $n$ if and only if…
We find a natural $L_{\omega_1,\omega}$-axiomatisation $\Sigma$ of a structure on the upper half-plane $\mathbb{H}$ as the covering space of modular curves. The main theorem states that $\Sigma$ has a unique model in every uncountable…
A cover of an associative (not necessarily commutative nor unital) ring $R$ is a collection of proper subrings of $R$ whose set-theoretic union equals $R$. If such a cover exists, then the covering number $\sigma(R)$ of $R$ is the…
We continue the study of computable embeddings for pairs of structures, i.e. for classes containing precisely two non-isomorphic structures. Surprisingly, even for some pairs of simple linear orders, computable embeddings induce a…
In this article we apply the results in the article "On Isolated Real Singularities I" to the study of real $ADE$-singularities. We show that said results enables us to find the homology groups of the Milnor fibres of real…
In this paper, we first discuss the structure of the Ramond N=2 superconformal algebras. Then we also classify the modules of the intermediate series over Ramond N=2 superconformal algebra.
We give a short uniform proof of centrality of $\mathrm K_2(\Phi,\,R)$ for all simply-laced root systems $\Phi$ of rank $\geq3$.
A relational structure is a core, if all its endomorphisms are embeddings. This notion is important for computational complexity classification of constraint satisfaction problems. It is a fundamental fact that every finite structure has a…
We find a remarkable family of $\mathrm{G}_2$ structures defined on certain principal $\mathrm{SO}(3)$-bundles $P_\pm\longrightarrow M$ associated with any given oriented Riemannian 4-manifold $M$. Such structures are always cocalibrated.…
We use forcing over admissible sets to show that, for every ordinal $\alpha$ in a club $C\subset\omega_1$, there are copies of $\alpha$ such that the isomorphism between them is not computable in the join of the complete $\Pi^1_1$ set…
Given a planar algebra we show the equivalence of the notions of a module over this algebra (in the operadic sense), and module over a universal annular algebra. We classify such modules, with invariant inner products, in the generic region…
We describe all binary simple homogeneous structures M in terms of 0-definable equivalence relations on M, which "coordinatize" M and control dividing, and extension properties that respect these equivalence relations.