Related papers: Main gap for locally saturated elementary submodel…
We generalize a well-known theorem binding the elementary equivalence relation on the level of PAC fields and the isomorphism class of their absolute Galois groups. Our results concern two cases: saturated PAC structures and non-saturated…
We study elementary submodels of a stable homogeneous structure. We improve the independence relation defined in [T. Hyttinen, On nonstructure of elementary submodels of a stable homogeneous structure, Fundamenta Mathematicae, 156(1998):…
We study when a union of saturated models is saturated in the framework of tame abstract elementary classes (AECs) with amalgamation. We prove: $\mathbf{Theorem}$ If $K$ is a tame AEC with amalgamation satisfying a natural definition of…
We study a free quantum motion on periodically structured manifolds composed of elementary two-dimensional "cells" connected either by linear segments or through points where the two cells touch. The general theory is illustrated with…
In this paper several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the…
Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.
We prove a version of a small index property theorem for strong amalgamation classes. Our result builds on an earlier theorem by Lascar and Shelah (in their case, for saturated models of uncountable first-order theories). We then study…
Our main result (Theorem 1) suggests a possible dividing line ($\mu$-superstable $+$ $\mu$-symmetric) for abstract elementary classes without using extra set-theoretic assumptions or tameness. This theorem illuminates the structural side of…
After the main gap theorem was proved (see [Sh:c]), in discussion, Harrington expressed a desire for a finer structure - of finitary character (when we have a structure theorem at all). I point out that the logic L_{infty,aleph_0}(d.q.)…
In this paper we prove: Theorem 1. Let $\mathcal{K}$ be an abstract elementary class which satisfies the joint embedding and amalgamation properties. Suppose $\lambda>\mu\geq LS(\mathcal{K})$ and $\theta$ is a limit ordinal $<\lambda^+$. If…
A paratopological group $G$ is saturated if the inverse $U^{-1}$ of each non-empty set $U\subset G$ has non-empty interior. It is shown that a [first-countable] paratopological group $H$ is a closed subgroup of a saturated (totally bounded)…
In the paper we consider the linear underdetermined system of a special type. Systems of this type appear in non-homogeneous network flow programming problems in the form of systems of constraints and can be characterized as systems with a…
This paper considers the problem of building saturated models for first-order graded logics. We define types as pairs of sets of formulas in one free variable which express properties that an element is expected, respectively, to satisfy…
Let K be an Abstract Elementary Class. Under the asusmptions that K has a nicely behaved forking-like notion, regular types and existence of some prime models we establish a decomposition theorem for such classes. The decomposition implies…
We apply the local removable singularity theorem for minimal laminations and the local picture theorem on the scale of topology to obtain two descriptive results for certain possibly singular minimal laminations of $\mathbb{R}^3$. These two…
Every transformation monoid comes equipped with a canonical topology-the topology of pointwise convergence. For some structures, the topology of the endomorphism monoid can be reconstructed from its underlying abstract monoid. This…
We derive the embedding structure of unitary N=2 minimal models and show as a result that these representations have a degeneration of uncharged singular states. This corrects some earlier mistakes made in the literature. We discuss the…
We show that if M is a stable unsuperstable homogeneous structure, then for most kappa < |M|, the number of elementary submodels of M of power kappa is 2^kappa .
We prove that for any homotopy type $X$, there is an abstract elementary class $\mathcal{C}$, with joint embedding, almagamation and no maximal models such that the classifying space realizes the homotopy type $X$. We provide a few explicit…
This paper focuses on the time-harmonic electromagnetic (EM) scattering problem in a general medium which may possess a nontrivial topological structure. We model this by an inhomogeneous and possibly anisotropic medium with embedded…