Extending Partial Orders on o-Minimal Structures to Definable Total Orders

Extending Partial Orders on O-minimal Structures to Deenable Total Orders

Structures Having O-minimal Open Core*

The open core of an expansion of a dense linear order is its reduct, in the sense of definability, generated by the collection of all of its open definable sets. In this paper, expansions of dense linear orders that have o-minimal open core are investigated, with emphasis on expansions of densely ordered groups. The first main result establishes conditions under which an expansion of a densely ...

A Simple Proof of the Marker-steinhorn Theorem for Expansions of Ordered Abelian Groups

We give a short and self-contained proof of the MarkerSteinhorn Theorem for o-minimal expansions of ordered groups, based on an analysis of linear orders definable in such structures.

The Lattice of Definable Equivalence Relations in Homogeneous $n$-Dimensional Permutation Structures

In Homogeneous permutations, Peter Cameron [Electronic Journal of Combinatorics 2002] classified the homogeneous permutations (homogeneous structures with 2 linear orders), and posed the problem of classifying the homogeneous ndimensional permutation structures (homogeneous structures with n linear orders) for all finite n. We prove here that the lattice of ∅-definable equivalence relations in ...

On orders induced by implications

In this paper, the orders induced by the residual implications obtained from uninorms are investigated. A necessary and sufficient condition is presented so that the ordinal sum of fuzzy implications satisfies the law of importation with a t-norm $T$. Some relationships between the orders induced by an ordinal sum implication and its summands are determined. The algebraic structures obtained fr...