Every definably complete expansion of an ordered field satisfies an analogue of the Baire Category Theorem.

Remark 4.2. For those familiar with category theory, one can define inverse limits for any category. In most cases the result will be another object of the same category (unique up to isomorphism), in which case the projection maps are then morphisms in that category. We will restrict our attention to the familiar categories of sets, groups, and rings. One can also generalize the index set {n} ...

Data often take the form of ordered categories. For instance, in education, test results are often reported as grades. Where a hierarchical structure exists for the data, multilevel modelling of such ordered categorisations can be carried out using macros in MLwiN. The ordered categorisation can be seen as the realisation of an unknown underlying latent variable. A link function is used to rela...

We will study the existence of different types of the Riesz Decomposition Property for the lexicographic product of two partially ordered groups. A special attention will be paid to the lexicographic product of the group of the integers with an arbitrary po-group. Then we apply these results to the study of n-perfect pseudo effect algebras. We show that the category of strong n-perfect pseudo-e...

This article presents a latent distribution model for the analysis of agreement on dichotomous or ordered category ratings. The model includes parameters that characterize bias, category definitions, and measurement error for each rater or test. Parameter estimates can be used to evaluate rater performance and to improve classification or measurement with use of multiple ratings. A simple maxim...

We extend the concept of constructive complete distributivity so as to make it applicable to ordered sets admitting merely bounded suprema The KZ doctrine for bounded suprema is of some independent interest and a few results about it are given The category of ordered sets admitting bounded suprema over which inhabited classically non empty in ma distribute is shown to be bi equivalent to a cate...

Monads are used for various applications in computer science, and well-known is e.g. the interpretation of morphisms in the Kleisli category of the term monad as variable substitutions assigning variables to terms. An application building upon this observation is the equivalence between most general unifiers and co-equalizers in this category [13]. In this paper we will use monads with addition...

In spite of increasing studies and investigations in the field of aggregation operators, there are two fundamental problems remaining unsolved: aggregation of L-fuzzy settheoretic notions and their justification. In order to solve these problems, we will formulate aggregation operators and their special types on partially ordered sets with universal bounds, and introduce their categories. Furth...

In this article we carry on the study of the fundamental category (Goubault and Raussen, 2002; Goubault, 2003) of a partially ordered topological space (Nachbin, 1965; Johnstone, 1982), as arising in e.g. concurrency theory (Fajstrup et al., 2006), initiated in (Fajstrup et al., 2004). The “algebra” of dipaths modulo dihomotopy (the fundamental category) of such a po-space is essentially finite...