This paper characterizes lexicographic preferences over alternatives that are identified by a finite number of attributes. Our characterization is based on two key concepts: weaker notion continuity called “mild continuity” (strict preference order between any different with respect to every attribute preserved around their small neighborhoods) and an “unhappy set” (any alternative outside such...

We generalize the main result of [K–K–S] concerning the convex embeddings of a chain Γ in a lexicographic power ∆Γ. For a fixed non-empty chain ∆, we derive necessary and sufficient conditions for the existence of non-empty solutions Γ to each of the lexicographic functorial equations (∆) ' Γ , (∆) ' Γ and (∆) ' Γ .

We study the Riesz decomposition property types of the lexicographic product of two po-groups. Then we apply them to the study of pseudo effect algebras which can be decomposed into a comparable system of non-void slices indexed by some subgroup of real numbers. Finally, we present their representation by the lexicographic product.

The words of a context-free language, ordered by the lexicographic ordering, form a context-free linear ordering. It is well-known that the linear orderings associated with deterministic context-free languages have a decidable monadic second-order theory. In stark contrast, we give an example of a context-free language whose lexicographic ordering has an undecidable first-order theory.

For any two linear orderings L and M , the representability number reprM (L) of L in M is the least ordinal α such that L can be orderembedded into the lexicographic power Mα lex. We study reprM (L) in the particular case that L is a lexicographic product and M is a Dedekindcomplete chain. Mathematics Subject Classification: Primary: 06A05; Secondary: 03E05, 54F05, 91B16

We prove that there exists no algorithm to decide whether the language generated by a context-free grammar is dense with respect to the lexicographic ordering. As a corollary to this result, we show that it is undecidable whether the lexicographic orderings of the languages generated by two context-free grammars have the same order type.

Received Revised ABSTRACT We show how to solve boolean combinations of inequations s > t in the Herbrand Universe, assuming that is interpreted as a lexicographic path ordering extending a total precedence. In other words, we prove that the existential fragment of the theory of a lexicographic path ordering which extends a total precedence is decidable.