Results 141 to 150 of about 1,136,955 (184)

Quasi-Stone Algebras

Mathematical Logic Quarterly, 1993
AbstractThe purpose of this paper is to define and investigate the new class of quasi‐Stone algebras (QSA's). Among other things we characterize the class of simple QSA's and the class of subdirectly irreducible QSA's. It follows from this characterization that the subdirectly irreducible QSA's form an elementary class and that the variety of QSA's is ...
Nalinaxi H. Sankappanavar, H. P. Sankappanavar   +1 more
semanticscholar   +3 more sources

Definable sets in Stone algebras

Archive for Mathematical Logic, 2016
The paper deals with definable sets of Stone algebras. The authors introduce the notion of pseudo o-minimality of a lattice-ordered structure and prove that the completion of the theory of Stone algebras is pseudo o-minimal. Thy also investigate the decomposition of Stone algebras and prove that any definable set of a Stone algebra is a union of ...
Lei Chen, Niandong Shi, G. Wu
semanticscholar   +2 more sources

The structure of algebraically and existentially closed Stone and double Stone algebras

Journal of Symbolic Logic, 1989
In this paper we study the varieties of Stone algebras (S, ∧, ∨, *, 0, 1) and double Stone algebras (D, ∧, ∨, *, +, 0, 1). Our primary interest is to give a structural description of the algebraically and existentially closed members of both classes. Our technique is an application of the natural dualities of Davey [6] and Clark and Krauss [5].
D. Clark
semanticscholar   +2 more sources

On a common abstraction of de Morgan algebras and Stone algebras

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1983
SynopsisWe consider a common abstraction of de Morgan algebras and Stone algebras which we call an MS-algebra. The variety of MS-algebras is easily described by adjoining only three simple equations to the axioms for a bounded distributive lattice.
T. Blyth, J. Varlet
semanticscholar   +3 more sources

Priestley Duality for Quasi-Stone Algebras

Studia Logica, 2000
The author describes the Priestley space of a quasi-Stone algebra in terms of a Priestley space with a certain equivalence relation. He shows that finite quasi-Stone algebras enjoy the amalgamation property and describes the Priestley space for free quasi-Stone algebras over a finite set.
H. Gaitán
semanticscholar   +2 more sources

Quantifier elimination for Stone algebras

Archive for Mathematical Logic, 1989
A Stone algebra is a distributive lattice with pseudocomplement that satisfies the Stone identity \(a^*\sqcup a^{**}=1\). The author determines all quantifier elimination classes of Stone algebras and all classes of Stone algebras that admit positive quantifier elimination (i.e.
Switgard Feuerstein
semanticscholar   +2 more sources

Post-like algebras and injective Stone algebras

Algebra Universalis, 1975
In [3] Balbes and Grw gave intrinsic and extrinsic characterizations of injective Stone algebras. Specifically, the injectives can be characterized (extrinsically) as those Stone algebras that are the direct product of a complete Boolean algebra with a complete Post algebra of order three.
R. Beazer
semanticscholar   +2 more sources

A 4-valued logic for double Stone algebras

International Journal of Approximate Reasoning
Arun Kumar, Neha Gaur, Bisham Dewan
exaly   +2 more sources

The decidability of some classes of Stone algebras

Algebra Universalis, 2012
Pavol Zlatoš
exaly   +3 more sources

Subdirectly irreducible and free Kleene-Stone algebras

Algebra Universalis, 1994
Fernando Guzman
exaly   +2 more sources