The poset product construction is used to derive embedding theorems for several classes of generalized basic logic algebras (GBL-algebras). In particular it is shown that every n-potent GBL-algebra is embedded in a poset product of finite n-potent MV-chains, and every normal GBL-algebra is embedded in a poset product of totally ordered GMV-algebras. Representable normal GBLalgebras have poset p...

A poset is called upper homogeneous (or "upho") if every principal order filter of the isomorphic to whole poset. We observe that rank and characteristic generating functions upho posets are multiplicative inverses one another.

We present a technique for destroying stationary subsets of Pκκ using partial square sequences. We combine this method with Gitik’s poset for changing the cofinality of a cardinal without adding bounded sets to prove a variety of consistency results concerning saturated ideals and the set S(κ, κ+). In this paper we continue our study of consistency results concerning the set S(κ, κ) = {a ∈ Pκκ ...

We construct an analogue of the normaliser decomposition for p–local finite groups (S,F ,L) with respect to collections of F –centric subgroups and collections of elementary abelian subgroups of S . This enables us to describe the classifying space of a p–local finite group, before p–completion, as the homotopy colimit of a diagram of classifying spaces of finite groups whose shape is a poset a...

For a stationary set S ⊆ ω1 and a ladder system C over S, a new type of gaps called C-Hausdorff is introduced and investigated. We describe a forcing model of ZFC in which, for some stationary set S, for every ladder C over S, every gap contains a subgap that is CHausdorff. But for every ladder E over ω1 \ S there exists a gap with no subgap that is E-Hausdorff. A new type of chain condition, c...

We define a poset of partitions associated to an operad. We prove that the operad is Koszul if and only if the poset is Cohen-Macaulay. In one hand, this characterisation allows us to compute the homology of the poset. This homology is given by the Koszul dual operad. On the other hand, we get new methods for proving that an operad is Koszul.

The special properties of planar posets have been studied, particularly in the 1970's by I. Rival and others. More recently, the connection between posets, their corresponding polynomial rings and corresponding simplicial complexes has been studied by R. Stanley and others. This paper, using work of A. Bjorner, provides a connection between the two bodies of work, by characterizing when planar...

We study flag enumeration in intervals in the uncrossing partial order on matchings. We produce a recursion for the cd-indices of intervals in the uncrossing poset Pn. We explicitly describe the matchings by constructing an order-reversing bijection. We obtain a recursion for the ab-indices of intervals in the poset P̂n, the poset Pn with a unique minimum 0̂ adjoined.