scholarly journals Longest common extension

2018 ◽  
Vol 68 ◽  
pp. 242-248 ◽  
Author(s):  
Béla Bollobás ◽  
Shoham Letzter
Keyword(s):  
Common Extension

Common extension of Boolean informational systems

1979 ◽  
Vol 2 (1) ◽  
pp. 63-70
Author(s):  
Tadeusz Traczyk
Keyword(s):  
Information Systems ◽  
Boolean Algebras ◽  
Numerical Characterization ◽  
Common Extension

The notion of numerical characterization of Boolean algebras and coproducts are used to define information systems and to develop the theory of such systems.

Two variable first-order logic over ordered domains

2001 ◽  
Vol 66 (2) ◽  
pp. 685-702 ◽  
Author(s):  
Martin Otto
Keyword(s):  
Order Logic ◽  
Decision Problems ◽  
First Order Logic ◽  
Satisfiability Problem ◽  
Exponential Time ◽  
Infinite Domains ◽  
First Order ◽  
Computation Tree ◽  
Common Extension ◽  
Undecidability Result

AbstractThe satisfiability problem for the two-variable fragment of first-order logic is investigated over finite and infinite linearly ordered, respectively wellordered domains, as well as over finite and infinite domains in which one or several designated binary predicates are interpreted as arbitrary wellfounded relations.It is shown that FO2 over ordered, respectively wellordered. domains or in the presence of one well-founded relation, is decidable for satisfiability as well as for finite satisfiability. Actually the complexity of these decision problems is essentially the same as for plain unconstrained FO2. namely non-deterministic exponential time.In contrast FO2 becomes undecidable for satisfiability and for finite satisfiability, if a sufficiently large number of predicates are required to be interpreted as orderings. wellorderings. or as arbitrary wellfounded relations. This undecidability result also entails the undecidability of the natural common extension of FO2 and computation tree logic CTL.

scholarly journals A Common Extension of Arhangel’skĭ’s Theorem and the Hajnal–Juhász Inequality

2020 ◽  
Vol 63 (1) ◽  
pp. 197-203 ◽  
Author(s):  
Angelo Bella ◽  
Santi Spadaro
Keyword(s):  
Hausdorff Space ◽  
Topological Spaces ◽  
Separation Axiom ◽  
Cardinal Invariants ◽  
Common Extension ◽  
Weak Lindelöf Number ◽  
Lindelöf Number

AbstractWe present a result about $G_{\unicode[STIX]{x1D6FF}}$ covers of a Hausdorff space that implies various known cardinal inequalities, including the following two fundamental results in the theory of cardinal invariants in topology: $|X|\leqslant 2^{L(X)\unicode[STIX]{x1D712}(X)}$ (Arhangel’skiĭ) and $|X|\leqslant 2^{c(X)\unicode[STIX]{x1D712}(X)}$ (Hajnal–Juhász). This solves a question that goes back to Bell, Ginsburg and Woods’s 1978 paper (M. Bell, J.N. Ginsburg and R.G. Woods, Cardinal inequalities for topological spaces involving the weak Lindelöf number, Pacific J. Math. 79(1978), 37–45) and is mentioned in Hodel’s survey on Arhangel’skiĭ’s Theorem (R. Hodel, Arhangel’skii’s solution to Alexandroff’s problem: A survey, Topology Appl. 153(2006), 2199–2217).In contrast to previous attempts, we do not need any separation axiom beyond $T_{2}$.

scholarly journals LEAN Production issues in the organization of the company - the first stage

2018 ◽  
Vol 21 (21) ◽  
pp. 36-39 ◽  
Author(s):  
Magdalena Mazur ◽  
Hassan Momeni
Keyword(s):  
Life Cycle ◽  
Dynamic Response ◽  
Product Life Cycle ◽  
Lean Production ◽  
Customer Requirements ◽  
Serial Production ◽  
Flexible Approach ◽  
Wide Range ◽  
Common Extension ◽  
Selection Of

Abstract Today’s market determinants and most importantly, very dynamically changing customer requirements significantly shortened the product life cycle. This situation reflects in companies by common extension of the assortment offered and personalised serial production. The result of a flexible approach to market changes is the implementation of LEAN concept, which, both in terms of management and production aims to develop efficiency within an organisation, which will then enable quick and dynamic response to changes in the environment. The popularity of LEAN concept (in management and production) among managers comes from its universality and a wide range of instruments used to maximise the use of existing potential. The main assumptions of LEAN concept are aimed at the maximum use of an organisation’s resources, defining the activities necessary to execute an order and identifying the areas generating losses and then minimising them and eventually eliminating. LEAN concept is based on flagship-main tools for identification and modernisation of processes, the difficulty in using them results from the need to recognise and select the most effective ones that meet the expectations of a given organisation. The article presents issues related to the first stage of implementing LEAN concept in a company’s structures, i.e. identification of opportunities and selection of appropriate tools.

Amalgamations preserving ℵ1-categoricity

1997 ◽  
Vol 62 (4) ◽  
pp. 1070-1074 ◽  
Author(s):  
Anand Pillay ◽  
Akito Tsuboi
Keyword(s):  
Equivalence Relation ◽  
Common Extension ◽  
The Universe

Let L0, L1 and L2 be countable languages with L ∩ L1 = L0. Let M0 be an L0-structure and Mi, an expansion of M0 to an Li,-structure (i = 1,2). We will call an L1 ∪ L2-structure M an amalgamation of M1 and M2 if M∣Li ≅ Mi, (i = 1,2). Let's consider the following problem.(*) Suppose that both M1 and M2 belong to the class . Can we always find an amalgamation M in ?Of course the existence of such an amalgamation depends on the class L. Some examples of and the answers are given below.1. = Countably saturated strongly minimal structures with the DMP In [3], Hrushovski showed that any two strongly minimal theories formulated in totally different languages have a common extension which is still strongly minimal and with the DMP (DMP is the property that states that if a point is sufficiently close to ā, then φ(, ) has the same rank and the same degree as φ(, ā).) His proof essentially shows that if L0 = ∅ then any two countably saturated strongly minimal structures with the DMP have a strongly minimal amalgamation. Also he gave an example that shows the condition L0 = ∅ is necessary.2. = ℵ1-categorical countable structures. Let M1 be the structure (ℚ, +) and let M2 be the {E, F}-structure defined by: (i) E is an equivalence relation which divides the universe into two infinite classes A and B, (ii) F is a bijection between A and B.

The lattice properties of 𝔛-local formations of finite groups

2020 ◽  
pp. 2150043 ◽  
Author(s):  
Aleksandr Tsarev
Keyword(s):  
Finite Groups ◽  
Simple Groups ◽  
Local Formation ◽  
Common Extension ◽  
Completeness Property

Let [Formula: see text] be a class of simple groups with a completeness property [Formula: see text]. Förster introduced the concept of [Formula: see text]-local formation in order to obtain a common extension of well-known theorems of Gaschütz–Lubeseder–Schmid and Baer [Publ. Mat. UAB 29(2–3) (1985) 39–76]. In this paper, it is proved that the lattice of all [Formula: see text]-local formations of finite groups is modular.

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