scholarly journals Decidability of Definability

2013 ◽  
Vol 78 (4) ◽  
pp. 1036-1054 ◽  
Author(s):  
Manuel Bodirsky ◽  
Michael Pinsker ◽  
Todor Tsankov
Keyword(s):  
Random Graph ◽  
Topological Dynamics ◽  
Homogeneous Structure ◽  
First Order ◽  
Computational Problem ◽  
Random Tournament ◽  
Universal Quantification ◽  
Countably Infinite ◽  
Existential Quantification

AbstractFor a fixed countably infinite structure Γ with finite relational signature τ, we study the following computational problem: input are quantifier-free τ-formulas ϕ0, ϕ1, …, ϕn that define relations R0, R1, …, Rn over Γ. The question is whether the relation R0 is primitive positive definable from R1, …, Rn, i.e., definable by a first-order formula that uses only relation symbols for R1, …, Rn, equality, conjunctions, and existential quantification (disjunction, negation, and universal quantification are forbidden).We show decidability of this problem for all structures Γ that have a first-order definition in an ordered homogeneous structure Δ with a finite relational signature whose age is a Ramsey class and determined by finitely many forbidden substructures. Examples of structures Γ with this property are the order of the rationals, the random graph, the homogeneous universal poset, the random tournament, all homogeneous universal C-relations, and many more. We also obtain decidability of the problem when we replace primitive positive definability by existential positive, or existential definability. Our proof makes use of universal algebraic and model theoretic concepts, Ramsey theory, and a recent characterization of Ramsey classes in topological dynamics.

scholarly journals A characterization of a topology on the countably infinite random graph

2002 ◽  
Vol 124 (3) ◽  
pp. 465-473
Author(s):  
Charles M. Grinstead ◽  
Louis M. Friedler
Keyword(s):  
Random Graph ◽  
Countably Infinite

scholarly journals On a stronger reconstruction notion for monoids and clones

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mike Behrisch ◽  
Edith Vargas-García
Keyword(s):  
Bipartite Graph ◽  
Random Graph ◽  
Ordered Set ◽  
Permutation Groups ◽  
Random Tournament ◽  
Automatic Homeomorphicity ◽  
Dense Group ◽  
Automatic Action ◽  
Transformation Monoids

Abstract Motivated by reconstruction results by Rubin, we introduce a new reconstruction notion for permutation groups, transformation monoids and clones, called automatic action compatibility, which entails automatic homeomorphicity. We further give a characterization of automatic homeomorphicity for transformation monoids on arbitrary carriers with a dense group of invertibles having automatic homeomorphicity. We then show how to lift automatic action compatibility from groups to monoids and from monoids to clones under fairly weak assumptions. We finally employ these theorems to get automatic action compatibility results for monoids and clones over several well-known countable structures, including the strictly ordered rationals, the directed and undirected version of the random graph, the random tournament and bipartite graph, the generic strictly ordered set, and the directed and undirected versions of the universal homogeneous Henson graphs.

Cylindric modal logic

1995 ◽  
Vol 60 (2) ◽  
pp. 591-623 ◽  
Author(s):  
Yde Venema
Keyword(s):  
Algebraic Logic ◽  
Equational Theory ◽  
Completeness Theorem ◽  
Cylindric Algebras ◽  
First Order ◽  
Finite Dimensional ◽  
Finite Dimensional Case ◽  
Existential Quantification ◽  
Cylindric Set Algebras

AbstractTreating the existential quantification ∃νi as a diamond ♢i and the identity νi = νj as a constant δij, we study restricted versions of first order logic as if they were modal formalisms. This approach is closely related to algebraic logic, as the Kripke frames of our system have the type of the atom structures of cylindric algebras; the full cylindric set algebras are the complex algebras of the intended multidimensional frames called cubes.The main contribution of the paper is a characterization of these cube frames for the finite-dimensional case and, as a consequence of the special form of this characterization, a completeness theorem for this class. These results lead to finite, though unorthodox, derivation systems for several related formalisms, e.g. for the valid n-variable first order formulas, for type-free valid formulas and for the equational theory of representable cylindric algebras. The result for type-free valid formulas indicates a positive solution to Problem 4.16 of Henkin, Monk and Tarski [16].

scholarly journals Characterization of Dissipative Structures for First-Order Symmetric Hyperbolic System with General Relaxation

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 728
Author(s):  
Yasunori Maekawa ◽  
Yoshihiro Ueda
Keyword(s):  
Hyperbolic System ◽  
Dissipative Structure ◽  
Dissipative Structures ◽  
Algebraic Characterization ◽  
Symmetric Hyperbolic System ◽  
Full Generality ◽  
Order Linear ◽  
First Order

In this paper, we study the dissipative structure of first-order linear symmetric hyperbolic system with general relaxation and provide the algebraic characterization for the uniform dissipativity up to order 1. Our result extends the classical Shizuta–Kawashima condition for the case of symmetric relaxation, with a full generality and optimality.

scholarly journals On Consensus Index of Triplex Star-Like Networks: A Graph Spectra Approach

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1248
Author(s):  
Da Huang ◽  
Jian Zhu ◽  
Zhiyong Yu ◽  
Haijun Jiang
Keyword(s):  
Algebraic Connectivity ◽  
Multi Agent Systems ◽  
Graph Spectra ◽  
Asymptotic Behaviors ◽  
Agent Systems ◽  
First Order ◽  
Laplacian Spectra ◽  
Multi Agent ◽  
Consensus Index

In this article, the consensus-related performances of the triplex multi-agent systems with star-related structures, which can be measured by the algebraic connectivity and network coherence, have been studied by the characterization of Laplacian spectra. Some notions of graph operations are introduced to construct several triplex networks with star substructures. The methods of graph spectra are applied to derive the network coherence, and some asymptotic behaviors of the indices have been derived. It is found that the operations of adhering star topologies will make the first-order coherence increase a constant value under the triplex structures as parameters tend to infinity, and the second-order coherence have some equality relations as the node related parameters tend to infinity. Finally, the consensus related indices of the triplex systems with the same number of nodes but non-isomorphic graph structures have been compared and simulated to verify the results.

scholarly journals Numerical Characterization of Cohesive and Non-Cohesive ‘Sediments’ under Different Consolidation States Using 3D DEM Triaxial Experiments

Processes ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1252
Author(s):  
Hadar Elyashiv ◽  
Revital Bookman ◽  
Lennart Siemann ◽  
Uri ten Brink ◽  
Katrin Huhn
Keyword(s):  
Mechanical Response ◽  
Burial Depth ◽  
Cohesive Sediments ◽  
Third Order ◽  
First Order ◽  
Numerical Characterization ◽  
Response To Stress ◽  
Bond Strengths ◽  
Individual Bond

The Discrete Element Method has been widely used to simulate geo-materials due to time and scale limitations met in the field and laboratories. While cohesionless geo-materials were the focus of many previous studies, the deformation of cohesive geo-materials in 3D remained poorly characterized. Here, we aimed to generate a range of numerical ‘sediments’, assess their mechanical response to stress and compare their response with laboratory tests, focusing on differences between the micro- and macro-material properties. We simulated two endmembers—clay (cohesive) and sand (cohesionless). The materials were tested in a 3D triaxial numerical setup, under different simulated burial stresses and consolidation states. Variations in particle contact or individual bond strengths generate first order influence on the stress–strain response, i.e., a different deformation style of the numerical sand or clay. Increased burial depth generates a second order influence, elevating peak shear strength. Loose and dense consolidation states generate a third order influence of the endmember level. The results replicate a range of sediment compositions, empirical behaviors and conditions. We propose a procedure to characterize sediments numerically. The numerical ‘sediments’ can be applied to simulate processes in sediments exhibiting variations in strength due to post-seismic consolidation, bioturbation or variations in sedimentation rates.

Amphibole and mica 40Ar/39Ar ages from the Kaipokok and Aillik domains, Makkovik Province, Labrador: towards a characterization of back-arc processes in the Paleoproterozoic

2002 ◽  
Vol 39 (5) ◽  
pp. 749-764 ◽  
Author(s):  
Nicholas Culshaw ◽  
Peter Reynolds ◽  
Gavin Sinclair ◽  
Sandra Barr
Keyword(s):  
Thermal Effect ◽  
Shear Zone ◽  
Second Order ◽  
Greenschist Facies ◽  
Metamorphic Rocks ◽  
Arc Magmatism ◽  
First Order ◽  
Back Arc ◽  
Order Pattern

We report amphibole and mica 40Ar/39Ar ages from the Makkovik Province. Amphibole ages from metamorphic rocks decrease towards the interior of the province, indicating a first-order pattern of monotonic cooling with progressive migration of the province into a more distal back-arc location. The amphibole data, in combination with muscovite ages, reveal a second-order pattern consisting of four stages corresponding to changing spatial and temporal configurations of plutonism and deformation. (1) The western Kaipokok domain cooled through muscovite closure by 1810 Ma, long after the cessation of arc magmatism. (2) The Kaipokok Bay shear zone, bounding the Kaipokok and Aillik domains, cooled through amphibole closure during 1805–1780 Ma, synchronous with emplacement of syn-tectonic granitoid plutons. (3) Between 1740 and 1700 Ma, greenschist-facies shearing occurred along the boundary between the Kaipokok domain and Nain Province synchronous with A-type plutonism and localized shearing in the western Kaipokok domain, cooling to muscovite closure temperatures in the Kaipokok Bay shear zone, and A-type plutonism and amphibole closure or resetting in the Aillik domain. (4) In the period 1650–1640 Ma, muscovite ages, an amphibole age from a shear zone, and resetting of plutonic amphibole indicate a thermal effect coinciding in part with Labradorian plutonism in the Aillik domain. Amphibole ages from dioritic sheets in the juvenile Aillik domain suggest emplacement between 1715 and 1685 Ma. Amphibole ages constrain crystallization of small mafic plutons in the Kaipokok domain (reworked Archean foreland) to be no younger than 1670–1660 Ma. These ages are the oldest yet obtained for Labradorian plutonism in the Makkovik Province.

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