scholarly journals WEAK SATURATION AND WEAK AMALGAMATION PROPERTY

2019 ◽  
Vol 84 (3) ◽  
pp. 929-936
Author(s):  
IVAN DI LIBERTI
Keyword(s):  
Model Theory ◽  
Existence And Uniqueness ◽  
Classical Model ◽  
Sufficient Conditions ◽  
Amalgamation Property ◽  
Accessible Categories ◽  
Image Position ◽  
Accessible Category ◽  
Weak Amalgamation

AbstractWe study the two model-theoretic concepts of weak saturation and weak amalgamation property in the context of accessible categories. We relate these two concepts providing sufficient conditions for existence and uniqueness of weakly saturated objects of an accessible category ${\cal K}$. We discuss the implications of this fact in classical model theory.

Universal domains and the amalgamation property

1993 ◽  
Vol 3 (2) ◽  
pp. 137-159 ◽  
Author(s):  
Manfred Droste ◽  
Rüdiger Gübel
Keyword(s):  
Programming Languages ◽  
Model Theory ◽  
Existence And Uniqueness ◽  
Denotational Semantics ◽  
Amalgamation Property ◽  
Large Classes ◽  
Semantics Of Programming Languages ◽  
Homogeneous Domains ◽  
Concrete Domains

In the theory of denotational semantics of programming languages, several authors have constructed various kinds of universal domains. We present here a categorical generalization of a well-known result in model theory, which we use to characterize large classes of reasonable categories that contain universal homogeneous objects. The existence of such objects is characterized by the condition that the finite objects in the category satisfy the amalgamation property. We derive from this the existence and uniqueness of universal homogeneous domains for several categories of bifinite domains, with embedding-projection-pairs as morphisms. We also obtain universal homogeneous objects for various categories of stable bifinite domains. In contrast, several categories of event domains and concrete domains and the category of all coherent Scott-domains do not contain universal homogeneous objects. Finally, we show that all our constructions can be performed effectively.

scholarly journals Abstract Beth definability in institutions

2006 ◽  
Vol 71 (3) ◽  
pp. 1002-1028 ◽  
Author(s):  
Marius Petria ◽  
Răzvan Diaconescu
Keyword(s):  
Model Theory ◽  
Science Studies ◽  
Classical Model ◽  
Sufficient Conditions ◽  
Abstract Model ◽  
Abstract Model Theory ◽  
The Third ◽  
Computing Science ◽  
Beth Definability ◽  
Partial Algebras

AbstractThis paper studies definability within the theory of institutions, a version of abstract model theory that emerged in computing science studies of software specification and semantics. We generalise the concept of definability to arbitrary logics, formalised as institutions, and we develop three general definability results. One generalises the classical Beth theorem by relying on the interpolation properties of the institution. Another relies on a meta Birkhoff axiomatizability property of the institution and constitutes a source for many new actual definability results, including definability in (fragments of) classical model theory. The third one gives a set of sufficient conditions for ‘borrowing’ definability properties from another institution via an ‘adequate’ encoding between institutions.The power of our general definability results is illustrated with several applications to (many-sorted) classical model theory and partial algebra, leading for example to definability results for (quasi-)varieties of models or partial algebras. Many other applications are expected for the multitude of logical systems formalised as institutions from computing science and logic.

PURE SEMISIMPLE FINITELY ACCESSIBLE CATEGORIES AND HERZOG'S CRITERION

2007 ◽  
Vol 06 (06) ◽  
pp. 1001-1025 ◽  
Author(s):  
A. I. CÁRCELES ◽  
J. L. GARCÍA
Keyword(s):  
Sufficient Conditions ◽  
Representation Type ◽  
Locally Finite ◽  
Finite Representation ◽  
Finite Representation Type ◽  
Artinian Rings ◽  
Semisimple Ring ◽  
Accessible Categories ◽  
Accessible Category ◽  
Necessary And Sufficient

Let [Formula: see text] be a finitely accessible category with products, and assume that its symmetric category [Formula: see text] is also finitely accessible and pure semisimple. We study necessary and sufficient conditions in both categories for [Formula: see text] (and hence [Formula: see text]) to be of locally finite representation type. In particular, we obtain a generalization of Herzog's criterion for finite representation type of left pure semisimple and right artinian rings. As an application, we prove that a left pure semisimple ring R with enough idempotents which has a self-duality is of locally finite representation type if and only if it is left locally finite.

scholarly journals Existence of Coupled Best Proximity Points of p-Cyclic Contractions

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 39
Author(s):  
Miroslav Hristov ◽  
Atanas Ilchev ◽  
Diana Nedelcheva ◽  
Boyan Zlatanov
Keyword(s):  
Wide Class ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Best Proximity Points ◽  
Cyclic Contractions ◽  
Ordered Pairs

We generalize the notion of coupled fixed (or best proximity) points for cyclic ordered pairs of maps to p-cyclic ordered pairs of maps. We find sufficient conditions for the existence and uniqueness of the coupled fixed (or best proximity) points. We illustrate the results with an example that covers a wide class of maps.

scholarly journals Correctness conditions for high-order differential equations with unbounded coefficients

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kordan N. Ospanov
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Order Linear Differential Equation ◽  
Unbounded Coefficients ◽  
Weighted Norms ◽  
Uniqueness Of The Solution ◽  
Linear Differential

AbstractWe give some sufficient conditions for the existence and uniqueness of the solution of a higher-order linear differential equation with unbounded coefficients in the Hilbert space. We obtain some estimates for the weighted norms of the solution and its derivatives. Using these estimates, we show the conditions for the compactness of some integral operators associated with the resolvent.

scholarly journals Horosphere slab separation theorems in manifolds without conjugate points

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Sameh Shenawy
Keyword(s):  
Euclidean Space ◽  
Hyperbolic Space ◽  
Existence And Uniqueness ◽  
Convex Set ◽  
Sufficient Conditions ◽  
Conjugate Points ◽  
Separation Theorems ◽  
Farthest Points ◽  
Simply Connected ◽  
Convex Subsets

Abstract Let $\mathcal {W}^{n}$ W n be the set of smooth complete simply connected n-dimensional manifolds without conjugate points. The Euclidean space and the hyperbolic space are examples of these manifolds. Let $W\in \mathcal {W}^{n}$ W ∈ W n and let A and B be two convex subsets of W. This note aims to investigate separation and slab horosphere separation of A and B. For example,sufficient conditions on A and B to be separated by a slab of horospheres are obtained. Existence and uniqueness of foot points and farthest points of a convex set A in $W\in \mathcal {W}$ W ∈ W are considered.

scholarly journals Existence and uniqueness in the theory of bending of elastic plates

1986 ◽  
Vol 29 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Christian Constanda
Keyword(s):  
Existence And Uniqueness ◽  
Integral Equation Method ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Equilibrium Equations ◽  
Dimensional Theory ◽  
Neumann Problems ◽  
Image Position

Kirchhoff's kinematic hypothesis that leads to an approximate two-dimensional theory of bending of elastic plates consists in assuming that the displacements have the form [1]In general, the Dirichlet and Neumann problems for the equilibrium equations obtained on the basis of (1.1) cannot be solved by the boundary integral equation method both inside and outside a bounded domain because the corresponding matrix of fundamental solutions does not vanish at infinity [2]. However, as we show in this paper, the method is still applicable if the asymptotic behaviour of the solution is suitably restricted.

scholarly journals Existence of Solutions of Nonlinear Stochastic Volterra Fredholm Integral Equations of Mixed Type

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
K. Balachandran ◽  
J.-H. Kim
Keyword(s):  
Integral Equations ◽  
Existence And Uniqueness ◽  
Mixed Type ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Stochastic Integral ◽  
Sufficient Conditions ◽  
Fredholm Integral Equations ◽  
Equations Of Mixed Type ◽  
Stochastic Integral Equations

We establish sufficient conditions for the existence and uniqueness of random solutions of nonlinear Volterra-Fredholm stochastic integral equations of mixed type by using admissibility theory and fixed point theorems. The results obtained in this paper generalize the results of several papers.

scholarly journals Existence and Uniqueness of Solutions to the Wage Equation of Dixit-Stiglitz-Krugman Model with No Restriction on Transport Costs

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Minoru Tabata ◽  
Nobuoki Eshima
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Nonlinear Operator ◽  
Sufficient Conditions ◽  
Wage Equation ◽  
Discrete Equation ◽  
Transport Costs ◽  
Economic Activities ◽  
Uniqueness Of Solutions ◽  
Double Nonlinear

In spatial economics, the distribution of wages is described by a solution to the wage equation of Dixit-Stiglitz-Krugman model. The wage equation is a discrete equation that has a double nonlinear singular structure in the sense that the equation contains a discrete nonlinear operator whose kernel itself is expressed by another discrete nonlinear operator with a singularity. In this article, no restrictions are imposed on the maximum of transport costs of the model and on the number of regions where economic activities are conducted. Applying Brouwer fixed point theorem to this discrete double nonlinear singular operator, we prove sufficient conditions for the wage equation to have a solution and a unique one.

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