scholarly journals AUTOMORPHISMS OF POWERS OF LINEARLY ORDERED SETS

2006 ◽  
Vol 14 (01) ◽  
pp. 77-85 ◽  
Author(s):  
CAROL L. WALKER ◽  
ELBERT A. WALKER
Keyword(s):  
Positive Integer ◽  
Partially Ordered Set ◽  
Automorphism Groups ◽  
Ordered Set ◽  
Unit Interval ◽  
Ordered Sets ◽  
Real Numbers ◽  
Main Interest ◽  
Partially Ordered ◽  
Usual Order

Let S be a bounded, partially ordered set, and n a positive integer. We investigate automorphism groups of Sn and of S[n], the non-decreasing n-tuples of Sn. Our main interest is in the case where S is the unit interval of real numbers with the usual order.

D-Continuity and Petri’s Axioms of Concurrency for Nonsequential Process Models

1987 ◽  
Vol 10 (2) ◽  
pp. 161-211
Author(s):  
Eike Best ◽  
Agathe Merceron
Keyword(s):  
Petri Nets ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Partially Ordered Sets ◽  
Process Models ◽  
Sequential Process ◽  
Ordered Sets ◽  
Related Property ◽  
Real Numbers ◽  
Partially Ordered

A non-sequential process can be modelled by a partially ordered set. Conversely, one is led to study the properties to be fulfilled by a poset so that it can reasonably be viewed as the model of a non-sequential process. To this end, C.A. Petri has proposed a set of con currency axioms and a related property called D-continuity, a generalised version for partially ordered sets of Dedekind’s completeness property of the real numbers. In this paper we study Petri’s axioms of concurrency and some of their interdependencies. We also derive several characterisations of D-continuity and exhibit its relation with the axioms of concurrency. Furthermore we apply our work to Petri nets: we introduce occurrence nets, some special posets which model the processes of a system net and we present their relations to D-continuity and the axioms of con currency. Finally we identify the class of the system nets whose processes are D-continuous and satisfy the axioms of concurrency.

Topologies of Lattice Products

1966 ◽  
Vol 18 ◽  
pp. 1004-1014 ◽  
Author(s):  
Richard A. Alo ◽  
Orrin Frink
Keyword(s):  
Direct Product ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Order Relation ◽  
Direct Products ◽  
Ordered Sets ◽  
Partially Ordered

A number of different ways of defining topologies in a lattice or partially ordered set in terms of the order relation are known. Three of these methods have proved to be useful and convenient for lattices of special types, namely the ideal topology, the interval topology, and the new interval topology of Garrett Birkhoff. In another paper (2) we have shown that these three topologies are equivalent for chains (totally ordered sets), where they reduce to the usual intrinsic topology of the chain.Since many important lattices are either direct products of chains or sublattices of such products, it is natural to ask what relationships exist between the various order topologies of a direct product of lattices and those of the lattices themselves.

scholarly journals Retracts of partially ordered sets

1979 ◽  
Vol 27 (4) ◽  
pp. 495-506 ◽  
Author(s):  
Dwight Duffus ◽  
Ivan Rival
Keyword(s):  
Fixed Points ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered

AbstractLet P be a finite, connected partially ordered set containing no crowns and let Q be a subset of P. Then the following conditions are equivalent: (1) Q is a retract of P; (2) Q is the set of fixed points of an order-preserving mapping of P to P; (3) Q is obtained from P by dismantling by irreducibles.

An Algebraic Aspect of Correspondences Between Implicational Fragment Logics and Fuzzy Logics

2015 ◽  
Vol 19 (6) ◽  
pp. 861-866
Author(s):  
Mayuka F. Kawaguchi ◽  
◽  
Michiro Kondo ◽  
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Unit Interval ◽  
Axiomatic System ◽  
Research Report ◽  
Algebraic Semantics ◽  
Fuzzy Logics ◽  
The Real ◽  
Partially Ordered ◽  
Algebraic Aspect

This research report treats a correspondence between implicational fragment logics and fuzzy logics from the viewpoint of their algebraic semantics. The authors introduce monotone BI-algebras by loosening the axiomatic system of BCK-algebras. We also extend the algebras of fuzzy logics with weakly-associative conjunction from the case of the real unit interval to the case of a partially ordered set. As the main result of this report, it is proved that the class of monotone BI-algebras with condition (S) coincides with the class of weakly-associative conjunctive algebras.

scholarly journals SUBLATTICES OF LATTICES OF ORDER-CONVEX SETS, II.

2003 ◽  
Vol 13 (05) ◽  
pp. 543-564 ◽  
Author(s):  
MARINA SEMENOVA ◽  
FRIEDRICH WEHRUNG
Keyword(s):  
Positive Integer ◽  
Partially Ordered Set ◽  
Convex Sets ◽  
Ordered Set ◽  
Finitely Based ◽  
Locally Finite ◽  
Partially Ordered ◽  
Finitely Based Variety ◽  
Atomistic Lattice ◽  
Convex Subsets

For a positive integer n, we denote by SUB (respectively, SUBn) the class of all lattices that can be embedded into the lattice Co(P) of all order-convex subsets of a partially ordered set P (respectively, P of length at most n). We prove the following results: (1) SUBn is a finitely based variety, for any n≥1. (2) SUB2 is locally finite. (3) A finite atomistic lattice L without D-cycles belongs to SUB if and only if it belongs to SUB2; this result does not extend to the nonatomistic case. (4) SUBn is not locally finite for n≥3.

CAYLEY GRAPHS OF PARTIALLY ORDERED SETS

2013 ◽  
Vol 12 (04) ◽  
pp. 1250184 ◽  
Author(s):  
MOJGAN AFKHAMI ◽  
ZAHRA BARATI ◽  
KAZEM KHASHYARMANESH
Keyword(s):  
Cayley Graph ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Cayley Graphs ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered ◽  
Basic Properties ◽  
Vertex Set

In this paper, we introduce the Cayley graph of a partially ordered set (poset). Let (P, ≤) be a poset, and let S be a subset of P. We define the undirected Cayley graph of P, denoted by Cay (P, S), as a graph with vertex-set P and edge-set E consisting of those sets {x, y} such that y ∈ {x, s}ℓ or x ∈ {y, s}ℓ for some s ∈ S, where for a subset T of P, Tℓ is the set of all x ∈ P such that x ≤ t, for all t ∈ T. We study some basic properties of Cay (P, S) such as connectivity, diameter and girth.

The Ordering of Spec R

1976 ◽  
Vol 28 (4) ◽  
pp. 820-835 ◽  
Author(s):  
William J. Lewis ◽  
Jack Ohm
Keyword(s):  
Commutative Ring ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Partially Ordered Sets ◽  
Prime Ideals ◽  
Ordered Sets ◽  
Partially Ordered

Let Specie denote the set of prime ideals of a commutative ring with identity R, ordered by inclusion; and call a partially ordered set spectral if it is order isomorphic to Spec R for some R. What are some conditions, necessary or sufficient, for a partially ordered set X to be spectral? The most desirable answer would be the type of result that would allow one to stare at the diagram of a given X and then be able to say whether or not X is spectral. For example, it is known that finite partially ordered sets are spectral (see [2] or [5]).

The superintuitionistic predicate logic of finite Kripke frames is not recursively axiomatizable

2005 ◽  
Vol 70 (2) ◽  
pp. 451-459 ◽  
Author(s):  
Dmitrij Skvortsov
Keyword(s):  
Partially Ordered Set ◽  
Possible Worlds ◽  
Ordered Set ◽  
Predicate Logic ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered ◽  
Kripke Frames ◽  
Finite Partially Ordered Set

AbstractWe prove that an intermediate predicate logic characterized by a class of finite partially ordered sets is recursively axiomatizable iff it is “finite”, i.e., iff it is characterized by a single finite partially ordered set. Therefore, the predicate logic LFin of the class of all predicate Kripke frames with finitely many possible worlds is not recursively axiomatizable.

Endomorphisms of Partially Ordered Sets

1998 ◽  
Vol 7 (1) ◽  
pp. 33-46
Author(s):  
DWIGHT DUFFUS ◽  
TOMASZ ŁUCZAK ◽  
VOJTĚCH RÖDL ◽  
ANDRZEJ RUCIŃSKI
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered

It is shown that every partially ordered set with n elements admits an endomorphism with an image of a size at least n1/7 but smaller than n. We also prove that there exists a partially ordered set with n elements such that each of its non-trivial endomorphisms has an image of size O((n log n)1/3).

Decidability and finite axiomatizability of theories of ℵ0-categorical partially ordered sets

1981 ◽  
Vol 46 (1) ◽  
pp. 101-120 ◽  
Author(s):  
James H. Schmerl
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Partially Ordered Sets ◽  
Finite Width ◽  
Ordered Sets ◽  
Partially Ordered ◽  
Decidable Theory ◽  
Axiomatizable Theory ◽  
Finitely Axiomatizable Theory

AbstractEvery ℵ0-categorical partially ordered set of finite width has a finitely axiomatizable theory. Every ℵ0-categorical partially ordered set of finite weak width has a decidable theory. This last statement constitutes a major portion of the complete (with three exceptions) characterization of those finite partially ordered sets for which any ℵ0-categorical partially ordered set not embedding one of them has a decidable theory.

Sign in / Sign up

Export Citation Format

Share Document