Amalgamation Property Research Articles

Some remarks on divisible polyhedral MV-algebras

AbstractBuilding on similar notions for MV-algebras, polyhedral DMV-algebras are defined and investigated. For such algebras dualities with suitable categories of polyhedra are established, and the relation with finitely presented Riesz MV-algebras is investigated. Via hull-functors, finite products are interpreted in terms of hom-functors, and categories of polyhedral MV-algebras, polyhedral DMV-algebras and finitely presented Riesz MV-algebras are linked together. Moreover, the amalgamation property is proved for finitely presented DMV-algebras and Riesz MV-algebras, and for polyhedral DMV-algebras.

Magnetic copper-ferrosilicon composites as regenerable sorbents for Hg0 removal

As a dangerous environmental pollutant, mercury is widely existed in coal-fired power plant gases. In this manuscript, a novel and reliable high-capacity adsorbent (MagFeSi-Cu°) was synthesized by powder metallurgy method to remove Hg° from flue gases. The FeSi, the nano-copper and the silica-coated magnetic Fe3O4 nanoparticles were mixed and calcinated at 300 °C by powder metallurgy method. Copper nanoparticles were uniformly dispersed on the FeSi surface by the linkage of Cu3Si, which was formed by the interfacial reaction between surface Cu atoms in the copper nanoparticles and the amorphous Si on the surface of FeSi. Due to the magnetic properties of the Fe3O4 nanoparticles, the adsorbent can be effectively separated from dust waste for further recycling and regeneration. The amorphous silicon in ferrosilicon (FeSi) reacts with copper nanoparticles, producing copper-silicon alloy as a binder to maintain the stability of copper nanoparticles. Besides that, well-dispersed copper nanoparticles prepared by liquid phase reduction have excellent amalgam properties. The characteristics mentioned above make the new composite (MagFeSi-Cu°) a regenerable sorbents for Hg° Removal from flue gas, which was confirmed by mercury removal test conducted in a fix-bed reactor.

EPPA for two-graphs and antipodal metric spaces

We prove that the class of finite two-graphs has the extension property for partial automorphisms (EPPA, or Hrushovski property), thereby answering a question of Macpherson. In other words, we show that the class of graphs has the extension property for switching automorphisms. We present a short, self-contained, purely combinatorial proof which also proves EPPA for the class of integer-valued antipodal metric spaces of diameter 3, answering a question of Aranda et al. The class of two-graphs is an important new example which behaves differently from all the other known classes with EPPA: Two-graphs do not have the amalgamation property with automorphisms (APA), their Ramsey expansion has to add a graph, it is not known if they have coherent EPPA, and even EPPA itself cannot be proved using the Herwig–Lascar theorem.

On the multi-dimensional modal logic of substitutions

Abstract We prove completeness, interpolation, decidability and an omitting types theorem for certain multi-dimensional modal logics where the states are not abstract entities but have an inner structure. The states will be sequences. Our approach is algebraic addressing varieties generated by complex algebras of Kripke semantics for such logics. The algebras dealt with are common cylindrification free reducts of cylindric and polyadic algebras. For finite dimensions, we show that such varieties are finitely axiomatizable, have the super amalgamation property, and that the subclasses consisting of only completely representable algebras are elementary, and are also finitely axiomatizable in first order logic. Also their modal logics have an N P complete satisfiability problem. Analogous results are obtained for infinite dimensions by replacing finite axiomatizability by finite schema axiomatizability.

Modeling the annealing and thermal stability of silver dental amalgam.

Effect of heat treatment on the structure and thermal properties of silver-copper dental amalgam (Ag-Cu/Hg) was investigated by means of Monte Carlo (MC) simulation. Simulated pair correlation functions in the framework of MC algorithm form the basis for a diverse analysis of the amalgam annealed up to 2893K. As heat treatment increases, structural properties remain essentially unchanged up to 1093K, beyond which, the properties are deteriorated. Phase separation in the context of homo-coordination and segregation of Ag-Cu alloy is characterized as the annealing of amalgam alloy is proceeded. Thus, the amalgam alloy could also maintain a microstructural phase and a structural strength around this temperature, consistent with the annealing reported experimentally. These findings provide insights into amalgam industrial technology, setting amalgamation process, Hg release in dental clinics, and basic information appreciated in the dentistry industry and partnership in forensic science. Graphical abstract Thermal stability of the homogeneous amalgam (Ag-Cu/Hg) is studied up to 2893 K where a phase separation and structural alteration is noted above 1093 and Hg phase segregates into a domain different from Ag-Cu alloy domain.

WEAK SATURATION AND WEAK AMALGAMATION PROPERTY

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.

Some aspects of topological Galois theory

We establish a number of results on the subject of the first author’s topos-theoretic generalization of Grothendieck’s Galois formalism. In particular, we generalize in this context the existence theorem of algebraic closures, we give a concrete description of the atomic completion of a small category whose opposite satisfies the amalgamation property, and we explore to which extent a model of a Galois-type theory is determined by its symmetries.

MTL-algebras as rotations of basic hoops

Abstract In this paper, we use the generalize d rotation construction to lift results from the lattice of subvarieties of basic hoops to some parts of the lattice of subvarieties of monoidal t-norm based logic-algebras. In particular, we study splitting algebras for (the lattice of subvarieties of) varieties generated by generalized rotations of basic hoops and relevant subvarieties such as Wajsberg hoops, cancellative hoops and Gödel hoops. Finally, we show that the generalized rotation construction preserves the amalgamation property.

The structure of random automorphisms of countable structures

In order to understand the structure of the `typical' element of an automorphism group, one has to study how large the conjugacy classes of the group are. When typical is meant in the sense of Baire category, a complete description of the size of the conjugacy classes has been given by Kechris and Rosendal. Following Dougherty and Mycielski we investigate the measure theoretic dual of this problem, using Christensen's notion of Haar null sets. When typical means random, that is, almost every with respect to this notion of Haar null sets, the behavior of the automorphisms is entirely different from the Baire category case. In this paper, we generalize the theorems of Dougherty and Mycielski about $S_\infty$ to arbitrary automorphism groups of countable structures isolating a new model theoretic property, the Cofinal Strong Amalgamation Property. As an application we show that a large class of automorphism groups can be decomposed into the union of a meager and a Haar null set.

AMALGAMABLE DIAGRAM SHAPES

AbstractA category has the amalgamation property (AP) if every pushout diagram has a cocone, and the joint embedding property (JEP) if every finite coproduct diagram has a cocone. We show that for a finitely generated category I, the following are equivalent: (i) every I-shaped diagram in a category with the AP and the JEP has a cocone; (ii) every I-shaped diagram in the category of sets and injections has a cocone; (iii) a certain canonically defined category ${\cal L}\left( {\bf{I}} \right)$ of “paths” in I has only idempotent endomorphisms. When I is a finite poset, these are further equivalent to: (iv) every upward-closed subset of I is simply-connected; (v) I can be built inductively via some simple rules. Our proof also shows that these conditions are decidable for finite I.

Epimorphisms of S-quantales

In this paper we study certain actions of a pomonoid S on a complete lattice, which we call S-quantales. Our aim is to characterize epimorphisms in the category of S-quantales. For this purpose we show that this category is a monadic construct and has the amalgamation property.

RELATIVELY EXCHANGEABLE STRUCTURES

AbstractWe study random relational structures that are relatively exchangeable—that is, whose distributions are invariant under the automorphisms of a reference structure ${M}$. When ${M}$ is ultrahomogeneous and has trivial definable closure, all random structures relatively exchangeable with respect to $m$ satisfy a general Aldous–Hoover-type representation. If ${M}$ also satisfies the n-disjoint amalgamation property (n-DAP) for all $n \ge 1$, then relatively exchangeable structures have a more precise description whereby each component depends locally on ${M}$.

An in vitro appraisal of properties of dental amalgam using commercially available and ayurvedically recycled mercury: Recycle and reuse.

Introduction:With the introduction of tooth-colored restoration material, the usage of amalgam has reduced over years. However, results regarding toxicity and health concerns are conflicting. Based on the concept of recycle and reuse, we previously used an ayurvedic method for purification of excess mercury obtained from dental operatory. In the present study, we aimed to evaluate the properties of dental amalgam using commercially available and ayurvedically recycled mercury.Materials and Methods:Samples were prepared for analysis of mean compressive strength, Vickers hardness number, and coefficient of friction dental amalgam using commercially available and ayurvedically recycled mercury. Further analysis was done using scanning electron microscopy. The data were presented on Microsoft Excel Spreadsheet 2013 and statistical analysis was done on IBM SPSS software (IBM Analytics) and OriginPro 8 software.Results and Conclusion:No statistically significant difference was found in properties of dental amalgam prepared using commercially available and ayurvedically recycled mercury. Although not statistically significant, early compressive strength and hardness of amalgam using ayurvedically recycled mercury were comparatively higher, which may be attributed to residual amounts of silver, tin, and copper acting as nucleating agent for faster setting reaction.

Non-absoluteness of model existence at $\aleph _\omega $

In [FHK13], the authors considered the question whether model-existence of $L_{\omega_1,\omega}$-sentences is absolute for transitive models of ZFC, in the sense that if $V \subseteq W$ are transitive models of ZFC with the same ordinals, $\varphi\in V$ and $V\models "\varphi \text{ is an } L_{\omega_1,\omega}\text{-sentence}"$, then $V \models "\varphi \text{ has a model of size } \aleph_\alpha"$ if and only if $W \models "\varphi \text{ has a model of size } \aleph_\alpha"$. From [FHK13] we know that the answer is positive for $\alpha=0,1$ and under the negation of CH, the answer is negative for all $\alpha>1$. Under GCH, and assuming the consistency of a supercompact cardinal, the answer remains negative for each $\alpha>1$, except the case when $\alpha=\omega$ which is an open question in [FHK13]. We answer the open question by providing a negative answer under GCH even for $\alpha=\omega$. Our examples are incomplete sentences. In fact, the same sentences can be used to prove a negative answer under GCH for all $\alpha>1$ assuming the consistency of a Mahlo cardinal. Thus, the large cardinal assumption is relaxed from a supercompact in [FHK13] to a Mahlo cardinal. Finally, we consider the absoluteness question for the $\aleph_\alpha$-amalgamation property of $L_{\omega_1,\omega}$-sentences (under substructure). We prove that assuming GCH, $\aleph_\alpha$-amalgamation is non-absolute for $1<\alpha<\omega$. This answers a question from [SS]. The cases $\alpha=1$ and $\alpha$ infinite remain open. As a corollary we get that it is non-absolute that the amalgamation spectrum of an $L_{\omega_1,\omega}$-sentence is empty.

GENERALIZED AMALGAMATION AND HOMOGENEITY

AbstractIn this paper we shall prove that any 2-transitive finitely homogeneous structure with a supersimple theory satisfying a generalized amalgamation property is a random structure. In particular, this adapts a result of Koponen for binary homogeneous structures to arbitrary ones without binary relations. Furthermore, we point out a relation between generalized amalgamation, triviality and quantifier elimination in simple theories.

Categorical equivalence and the Ramsey property for finite powers of a primal algebra

In this paper, we investigate the best known and most important example of a categorical equivalence in algebra, that between the variety of boolean algebras and any variety generated by a single primal algebra. We consider this equivalence in the context of Kechris-Pestov-Todorcevic correspondence, a surprising correspondence between model theory, combinatorics and topological dynamics. We show that relevant combinatorial properties (such as the amalgamation property, Ramsey property and ordering property) carry over from a category to an equivalent category. We then use these results to show that the category whose objects are isomorphic copies of finite powers of a primal algebra $${\mathcal{A}}$$ together with a particular linear ordering <, and whose morphisms are embeddings, is a Ramsey age (and hence a Fraisse age). By the Kechris-Pestov-Todorcevic correspondence, we then infer that the automorphism group of its Fraisse limit is extremely amenable. This correspondence also enables us to compute the universal minimal flow of the Fraisse limit of the class $${{\bf V}_{fin} \mathcal{(A)}}$$ whose objects are isomorphic copies of finite powers of a primal algebra $${\mathcal{A}}$$ and whose morphisms are embeddings.

Topological Ramsey spaces from Fraïssé classes, Ramsey-classification theorems, and initial structures in the Tukey types of p-points

A general method for constructing a new class of topological Ramsey spaces is presented. Members of such spaces are infinite sequences of products of Fraisse classes of finite relational structures satisfying the Ramsey property. The Product Ramsey Theorem of Sokic is extended to equivalence relations for finite products of structures from Fraisse classes of finite relational structures satisfying the Ramsey property and the Order-Prescribed Free Amalgamation Property. This is essential to proving Ramsey-classification theorems for equivalence relations on fronts, generalizing the Pudlak–Rodl Theorem to this class of topological Ramsey spaces. To each topological Ramsey space in this framework corresponds an associated ultrafilter satisfying some weak partition property. By using the correct Fraisse classes, we construct topological Ramsey spaces which are dense in the partial orders of Baumgartner and Taylor (Trans Am Math Soc 241:283–309, 1978) generating p-points which are k-arrow but not $$k+1$$ -arrow, and in a partial order of Blass (Trans Am Math Soc 179:145–166, 1973) producing a diamond shape in the Rudin-Keisler structure of p-points. Any space in our framework in which blocks are products of n many structures produces ultrafilters with initial Tukey structure exactly the Boolean algebra $$\mathcal {P}(n)$$ . If the number of Fraisse classes on each block grows without bound, then the Tukey types of the p-points below the space’s associated ultrafilter have the structure exactly $$[\omega ]^{<\omega }$$ . In contrast, the set of isomorphism types of any product of finitely many Fraisse classes of finite relational structures satisfying the Ramsey property and the OPFAP, partially ordered by embedding, is realized as the initial Rudin-Keisler structure of some p-point generated by a space constructed from our template.

Shelah’s eventual categoricity conjecture in universal classes: part II

We prove that a universal class categorical in a high-enough cardinal is categorical on a tail of cardinals. As opposed to other results in the literature, we work in ZFC, do not require the categoricity cardinal to be a successor, do not assume amalgamation, and do not use large cardinals. Moreover we give an explicit bound on the "high-enough" threshold: $\mathbf{Theorem}$ Let $\psi$ be a universal $\mathbb{L}_{\omega_1, \omega}$ sentence. If $\psi$ is categorical in some $\lambda \ge \beth_{\beth_{\omega_1}}$, then $\psi$ is categorical in all $\lambda' \ge \beth_{\beth_{\omega_1}}$. As a byproduct of the proof, we show that a conjecture of Grossberg holds in universal classes: $\mathbf{Corollary}$ Let $\psi$ be a universal $\mathbb{L}_{\omega_1, \omega}$ sentence that is categorical in some $\lambda \ge \beth_{\beth_{\omega_1}}$, then the class of models of $\psi$ has the amalgamation property for models of size at least $\beth_{\beth_{\omega_1}}$. We also establish generalizations of these two results to uncountable languages. As part of the argument, we develop machinery to transfer model-theoretic properties between two different classes satisfying a compatibility condition. This is used as a bridge between Shelah's milestone study of universal classes (which we use extensively) and a categoricity transfer theorem of the author for abstract elementary classes that have amalgamation, are tame, and have primes over sets of the form $M \cup \{a\}$.

Functorial semantics of first-order views

We provide a precise mathematical definition for first-order views used in parameterised specifications and we also provide a dual semantics for them that captures both their syntactic and model theoretic effects. We show that this semantics is functorial. Parameter instantiation is defined here as a (special kind of) pushout in the category of views; moreover the corresponding pushout squares are shown to enjoy a crucial model amalgamation property that ensures the consistency of the parameter instantiation process.

The Robinson property and amalgamations of higher arities

In this article we discuss a version of the Robinson property studied recently by Gyenis in , and we present a solution to one of his open problems. We say that a first‐order structure satisfies the Robinson property whenever the union of two non‐trivial partial n‐types over different finite sets is realizable if and only if they are not explicitly contradictory. In his article, Gyenis showed that a universal, homogeneous structure over a language that consists of at most binary relation symbols satisfies the Robinson property if and only if its age has a generalized amalgamation property (the so called prescribed amalgamation property, PAP). We go further and define a series of new kinds of amalgamation properties, APn for any natural number n. Using these properties we can characterize all universal and homogeneous structures that satisfy the Robinson property independently from the arities of relation symbols of the language.