We show that whenever A is a monotone σ-complete dimension group, then A+ ∪ {∞} is countably equationally compact, and we show how this property can supply the necessary amount of completeness in several kinds of problems. In particular, if A is a countable dimension group and E is a monotone σ-complete dimension group, then the ordered group of all relatively bounded homomorphisms from A to E ...

We find necessary and sufficient conditions for a complete local (Noetherian) ring containing the rationals to be completion of countable excellent domain. Furthermore, we noncatenary domain, as well it unique factorization

We study the set of depths of relative algebras of countable Boolean algebras, in particular the extent to which this set may not be downward closed within the countable ordinals for a fixed countable Boolean algebra. Doing so, we exhibit a structural difference between the class of arbitrary rank countable Boolean algebras and the class of rank one countable Boolean algebras.

Abstract Stone Duality is a revolutionary theory that works directly with computable continuous functions, without using set theory, infinitary lattice theory or a prior theory of discrete computation. Every expression in the calculus denotes both a continuous function and a program, but the reasoning looks remarkably like a sanitised form of that in classical topology. This paper is an introdu...

In recent years, much work in descriptive set theory has been focused on the Borel complexity of naturally occurring classification problems, in particular, the study of countable Borel equivalence relations and their structure under the quasi-order of Borel reducibility. Following the approach of Louveau and Rosendal for the study of analytic equivalence relations, we study countable Borel qua...

The concept of intuitionistic fuzzy β-almost compactness and intuitionistic fuzzy β-nearly compactness in intuitionistic fuzzy topological spaces is introduced and studied. Besides giving characterizations of these spaces, we study some of their properties. Also, we investigate the behavior of intuitionistic fuzzy β-compactness, intuitionistic fuzzy β-almost compactness, and intuitionistic fuzz...

A theory formulated in a countable predicate calculus can have at most 2א0 nonisomorphic countable models. In 1961 R. L. Vaught [9] conjected that if such a theory has uncountably many countable models, then it has exactly 2א0 countable models. This would of course follow immediately if one assumed the continuum hypothesis to be true. Almost ten years later, M. Morley [5] proved that if a count...

A variant of compactness designated as statistical has been introduced. Statistically compact subsets n-dimensional Euclidean space Rn have characterized by using Cantor-Bendixson derivative and it is further extended to the product RN.