A STRONG PROPERTY OF THE WEAK SUBALGEBRA LATTICE FOR LOCALLY FINITE ALGEBRAS OF FINITE TYPE

2013 ◽  
Vol 23 (01) ◽  
pp. 1-35
Author(s):  
KONRAD PIÓRO
Keyword(s):  
Finite Type ◽  
Locally Finite ◽  
Finite Algebras ◽  
Edge Disjoint ◽  
Subalgebra Lattice ◽  
Strong Property ◽  
Directed Hypergraphs ◽  
Algebraic Result ◽  
Directed Hypergraph

The aim of this paper is to show that the weak subalgebra lattice uniquely determines the subalgebra lattice for locally finite algebras of a fixed finite type. However, this algebraic result turns out to be a very particular case of the following hypergraph result (which is interesting itself): A total directed hypergraph D of finite type is uniquely determined, in the class of all the directed hypergraphs of this type, by its skeleton up to the orientation of some pairwise edge-disjoint directed hypercycles and hyperpaths. The skeleton of D is a hypergraph obtained from D by omitting the orientation of all edges.

scholarly journals The Planarity Theorems of MacLane and Whitney for Graph-like Continua

10.37236/284 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Robin Christian ◽  
R. Bruce Richter ◽  
Brendan Rooney
Keyword(s):  
Finite Graph ◽  
Disjoint Paths ◽  
Locally Finite ◽  
Edge Disjoint ◽  
Locally Finite Graph ◽  
Compact Graph

The planarity theorems of MacLane and Whitney are extended to compact graph-like spaces. This generalizes recent results of Bruhn and Stein (MacLane's Theorem for the Freudenthal compactification of a locally finite graph) and of Bruhn and Diestel (Whitney's Theorem for an identification space obtained from a graph in which no two vertices are joined by infinitely many edge-disjoint paths).

An algebraic result about soft model theoretical equivalence relations with an application to H. Friedman's fourth problem

1981 ◽  
Vol 46 (3) ◽  
pp. 523-530 ◽  
Author(s):  
Daniele Mundici
Keyword(s):  
Finite Type ◽  
Equivalence Relations ◽  
Algebraic Characterization ◽  
Elementary Equivalence ◽  
Algebraic Result ◽  
Theoretical Equivalence ◽  
Skolem Theorem

AbstractWe prove the following algebraic characterization of elementary equivalence: ≡ restricted to countable structures of finite type is minimal among the equivalence relations, other than isomorphism, which are preserved under reduct and renaming and which have the Robinson property; the latter is a faithful adaptation for equivalence relations of the familiar model theoretical notion. We apply this result to Friedman's fourth problem by proving that if is an (ω1, ω)-compact logic satisfying both the Robinson consistency theorem on countable structures of finite type and the Löwenheim-Skolem theorem for some λ < ωω for theories having ω1 many sentences, then ≡L = ≡ on such structures.

Varieties that make one Cross

1978 ◽  
Vol 26 (3) ◽  
pp. 368-382 ◽  
Author(s):  
Sheila Oates MacDonald ◽  
M. R. Vaughan-Lee
Keyword(s):  
Minimal Condition ◽  
Variety Of Algebras ◽  
Finite Variety ◽  
Associative Algebras ◽  
Maximal Condition ◽  
Locally Finite ◽  
Finite Algebras ◽  
Locally Finite Variety

AbstractAn example is constructed of a locally finite variety of non-associative algebras which satisfies the maximal condition on subvarieties but not the minimal condition. Based on this, counterexamples to various conjectures concerning varieties generated by finite algebras are constructed. The possibility of finding a locally finite variety of algebras which satisfies the minimal condition on subvarieties but not the maximal is also investigated.

scholarly journals Congruence lattices of locally finite algebras

2005 ◽  
Vol 54 (2) ◽  
pp. 237-248 ◽  
Author(s):  
Keith A. Kearnes
Keyword(s):  
Locally Finite ◽  
Finite Algebras ◽  
Congruence Lattices

Non-simply connected H-spaces with finiteness conditions

2001 ◽  
Vol 130 (3) ◽  
pp. 475-488 ◽  
Author(s):  
CARLES BROTO ◽  
JUAN A. CRESPO ◽  
LAIA SAUMELL
Keyword(s):  
Finite Type ◽  
Transcendence Degree ◽  
Cohomology Algebra ◽  
Finiteness Conditions ◽  
Locally Finite ◽  
Simply Connected

This article is concerned with homotopy properties of H-spaces X that are reflected in the module of indecomposables QH*(X; [ ]p). It is shown that mod p H-spaces X of finite type with finite transcendence degree mod p cohomology and locally finite QH*(X; [ ]p) are Bℤ/p-null spaces, Eilenberg–MacLane spaces K(ℤˆp, 2), K(ℤ/pr, 1), and extensions of those. If we restrict attention to H-spaces with noetherian mod p cohomology algebra, then we are left with finite mod p H-spaces and Eilenberg–MacLane spaces.

scholarly journals Decidable discriminator varieties from unary varieties

1991 ◽  
Vol 56 (4) ◽  
pp. 1355-1368 ◽  
Author(s):  
Stanley Burris ◽  
Ralph Mckenzie ◽  
Matthew Valeriote
Keyword(s):  
Finite Type ◽  
Locally Finite ◽  
Decidable Theory ◽  
Discriminator Varieties ◽  
Locally Finite Varieties

AbstractWe determine precisely those locally finite varieties of unary algebras of finite type which, when augmented by a ternary discriminator, generate a variety with a decidable theory.

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