Stone Algebras

 

Title: Stone Algebras
Author: Walter Guttmann
Submission date: 2016-09-06
Abstract: A range of algebras between lattices and Boolean algebras generalise the notion of a complement. We develop a hierarchy of these pseudo-complemented algebras that includes Stone algebras. Independently of this theory we study filters based on partial orders. Both theories are combined to prove Chen and Gr├Ątzer's construction theorem for Stone algebras. The latter involves extensive reasoning about algebraic structures in addition to reasoning in algebraic structures.
BibTeX:
@article{Stone_Algebras-AFP,
  author  = {Walter Guttmann},
  title   = {Stone Algebras},
  journal = {Archive of Formal Proofs},
  month   = sep,
  year    = 2016,
  note    = {\url{http://isa-afp.org/entries/Stone_Algebras.shtml},
            Formal proof development},
  ISSN    = {2150-914x},
}
License: BSD License
Used by: Stone_Relation_Algebras
Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.