In this paper, we show that the correspondence discovered by Koshevoy (1999) and, Johnson and Dean (1998) between anti-exchange closure operators and path independent choice operators is a duality between two semilattices of such operators. Then we use this duality to obtain old and new results...

For a given finite poset (P,-<), we construct strict completions of P which are models of all finite lattices L such that the set of join-irreducible elements of L is isomorphic to P.

We present a survey of properties of the lattice of closure systems (families of subsets of a set S containing S and closed by set intersection) on a finite set S with proofs of the more significant results. In particular, we prove that this lattice is atomistic and lower bounded and that there...

In this paper, we show that the correspondence discovered by Koshevoy ([18]) and Johnson and Dean ([15],[16]) between anti-exchange closure operators and path independent choice operators is a duality between two semilattices of such operators. Then we use this duality to obtain results...