Related papers: On perturbations of continuous structures
An isomorphism of symplectically tame smooth pseudocomplex structures on the complex projective plane which is a homeomorphism and differentiable of full rank at two points is smooth.
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
When a solution to an abstract inverse linear problem on Hilbert space is approximable by finite linear combinations of vectors from the cyclic subspace associated with the datum and with the linear operator of the problem, the solution is…
We prove that many seemingly simple theories have Borel complete reducts. Specifically, if a countable theory has uncountably many complete 1-types, then it has a Borel complete reduct. Similarly, if $Th(M)$ is not small, then $M^{eq}$ has…
We study the fluted fragment of first-order logic which is often viewed as a multi-variable non-guarded extension to various systems of description logics lacking role-inverses. In this paper we show that satisfiable fluted sentences (even…
The paper has a form of a talk on the given topic. It consists of three parts. The first part of the paper contains main notions, the second one is devoted to logical geometry, the third part describes types and isotypeness. The problems…
Necessary and sufficient conditions are given for the similarity between two perturbations of the (backward) shift by rank one operators, under certain assumptions on the perturbations. The proof of similarity is based on an explicit…
Linear topological spaces with partial ordering (linear kinematics) are studied. They are defined by a set of 8 axioms implying that topology, linear structure and ordering are compatible with each other. Most of the results are valid for…
We develop a structure theory of connected solvable spherical subgroups in semisimple algebraic groups. Based on this theory, we obtain an explicit classification of all such subgroups up to conjugation.
We survey the logical structure of constructive set theories and point towards directions for future research. Moreover, we analyse the consequences of being extensible for the logical structure of a given constructive set theory. We…
Simple type theory is suited as framework for combining classical and non-classical logics. This claim is based on the observation that various prominent logics, including (quantified) multimodal logics and intuitionistic logics, can be…
We study $\varepsilon$-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
We study the framework of abductive logic programming extended with integrity constraints. For this framework, we introduce a new measure of the simplicity of an explanation based on its degree of \emph{arbitrariness}: the more arbitrary…
We consider mappings satisfying a certain estimate of the distortion of the modulus of families of paths, similar to the geometric definition of quasiconformal mappings. Under appropriate restrictions, we show that the class of such…
The ultraproduct construction is generalized to $p$-ultramean constructions ($1\leqslant p<\infty$) by replacing ultrafilters with finitely additive measures. These constructions correspond to the linear fragments $\mathscr L^p$ of…
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded perturbation is considered. The objective is to estimate the norm of the difference of two spectral projections associated with isolated parts…
In this paper we establish asymptotic (biasymptotic) equivalence between spaces of solutions of a given linear homogeneous system and a perturbed system. The perturbations are of either linear or weakly linear characters. Existence of a…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…