Les chaínes complêtes sont simplifiables à droite pour la multiplication ordinale
Linear extensions of orders invariant under abelian group actions
Let G be an abelian group acting on a set X, and suppose that no element of G has any finite orbit of size greater than one. We show that every partial order on X invariant under G extends to a linear order on X also invariant under G. We then discuss extensions to linear preorders when the orbit condition is not met, and show that for any abelian group acting on a set X, there is a linear preorder ≤ on the powerset 𝓟X invariant under G and such that if A is a proper subset of B, then A < B...
Minimality of non-σ-scattered orders
We will characterize-under appropriate axiomatic assumptions-when a linear order is minimal with respect to not being a countable union of scattered suborders. We show that, assuming PFA⁺, the only linear orders which are minimal with respect to not being σ-scattered are either Countryman types or real types. We also outline a plausible approach to demonstrating the relative consistency of: There are no minimal non-σ-scattered linear orders. In the process of establishing these results, we will...
Note on canonizing ordering theorems for Hales Jewett structures
Note on compatible well orders on a free monoid.
Note on quasi-orders, partial orders and orders
-idéaux des ensembles ordonnés
O riešení niektorých nerozhodnutelných topologických problémov
OCA and towers in
We shall show that Open Coloring Axiom has different influence on the algebra than on . The tool used to accomplish this is forcing with a Suslin tree.
On a property of partially ordered sets.
On a Theory of Scale Types.
On chains and posets within the power set of a continuum.
On chains whose power semigroups are lattices.
On extensions of cyclic orders
On some hypotheses concerning trees.
On Some Intercalations In Ordered Sets
On the characterization of semilattices satisfying the descending chain condition and some remarks on distinguishing subsets
On the Order Type L-valued Relations on L-powersets.
Order Preserving or Increasing Mappings Freedom or Incomparability Preserving Mappings
Ordres à distance minimum d'un tournoi et graphes partiels sans circuits maximaux