The completion of a poset in a lattice of antichains. / Crampton, J.; Loizou, G.

In: International Mathematical Journal, Vol. 1, No. 3, 2001, p. 223-238.

Research output: Contribution to journalArticle



It is well known that given a poset, $X$, the lattice of order ideals of $X$, $ixsubseteq$, is a completion of $X$ via the order-embedding $X hookrightarrow where $x) = x$. Herein we define a lattice of antichains in $X$, $axpe$, and prove it is isomorphic to $ixsubseteq$. We establish the ``join'' and ``meet'' operations of the lattice, and present results for $axpe$ analogous to standard results for $ixsubseteq$, including Birkhoff's Representation Theorem for finite distributive lattices and a Dedekind-MacNeille-style completion using antichains. We also discuss the relevance and application of completions using antichains to access control in computer science, in particular with reference to role-based access control and to modelling conflict of interest policies.
Original languageEnglish
Pages (from-to)223-238
Number of pages16
JournalInternational Mathematical Journal
Issue number3
Publication statusPublished - 2001

ID: 1275124