Related papers: On the uniqueness property of forking in abstract …
In this paper we examine the task set forth by Shelah and Villaveces in \cite{ShVi} of proving the uniqueness of limit models of cardinality $\mu$ in $\lambda$-categorical abstract elementary classes with no maximal models, where $\lambda$…
We classify all apartness relations definable in propositional logics extending intuitionistic logic using Heyting algebra semantics. We show that every Heyting algebra which contains a non-trivial apartness term satisfies the weak law of…
The class of $\mu$-compact sets can be considered as a natural extension of the class of compact metrizable subsets of locally convex spaces, to which the particular results well known for compact sets can be generalized. This class…
For an arbitrary category, we consider the least class of functors con- taining the projections and closed under finite products, finite coproducts, parameterized initial algebras and parameterized final coalgebras, i.e. the class of…
We classify static manifolds which admit more than one static decomposition whenever a condition on the curvature is fullfilled. For this, we take a standard static vector field and analyze its associated one parameter family of projections…
We extend effective field theory to the case of spontaneous symmetry breaking in genuinely finite quantum systems such as small superfluid systems, molecules or atomic nuclei, and focus on deformed nuclei. In finite superfluids, symmetry…
The cofinality quantifiers were introduced by Shelah as an example of a compact logic stronger than first-order logic. We show that the classes of models axiomatized by these quantifiers can be turned into an Abstract Elementary Class by…
We present a novel notion of stable objects in a triangulated category. This Postnikov-stability is preserved by equivalences. We show that for the derived category of a projective variety this notion includes the case of semistable…
In this survey-research paper, we first introduce the theory of Smith classes of complexes with fixed-point free, periodic maps on them. These classes, when defined for the deleted product of a simplicial complex $K$, are the same as the…
The split property of a pure state for a certain cut of a quantum spin system can be understood as the entanglement between the two subsystems being weak. From this point of view, we may say that if it is not possible to transform a state…
We show that the class of representable substitution algebras is characterized by a set of universal first order sentences. In addition, it is shown that a necessary and sufficient condition for a substitution algebra to be representable is…
Algebraic geometry, although little explored in signal processing, provides tools that are very convenient for investigating generic properties in a wide range of applications. Generic properties are properties that hold "almost…
We prove conditional weak-strong uniqueness of the potential Euler solution for external flow around a smooth body in three space dimensions, within the class of viscosity weak solutions with the same initial data. Our sufficient condition…
In his seminal Inventiones paper from 1972 Grauert proved the existence of a semiuniversal deformation of an arbitrary complex analytic isolated singularity. For the proof he invented an approximation theorem for solving a system of…
The reader surely knows what particles physics is about: finding building blocks of nature that appear elementary at a given time and study their interactions - so why in the world this essay? The problem is how to arrive at a fundamental…
We introduce some deformations of the biset category and prove a semisimplicity property. We also consider another group category, called the subgroup category, whose morphisms are subgroups of direct products, the composition being star…
Inertial manifold theory, saddle point property and exponential dichotomy have been treated as different topics in the literature with different proofs. As a common feature, they all have the purpose of `splitting' the space to understand…
Taking residual finiteness as a starting point, we consider three related finiteness properties: weak subsemigroup separability, strong subsemigroup separability and complete separability. We investigate whether each of these properties is…
We consider Shimura varieties associated to a unitary group of signature $(n-s,s)$ where $n$ is even. For these varieties, by using the spin splitting models from Zachos-Zhao, we construct flat, Cohen-Macaulay, and normal $p$-adic integral…
In this paper, we exhibit the equivalence between different notions of unique range sets, namely, unique range sets, weighted unique range sets and weak-weighted unique range sets under certain conditions.\par Also, we present some…