Compactness and homogeneity of saturated structures. I.
Compactness and homogeneity of saturated structures. II.
Compactness and homomorphisms of algebraic structures
Compactness and Löwenheim-Skolem properties in categories of pre-institutions
The abstract model-theoretic concepts of compactness and Löwenheim-Skolem properties are investigated in the "softer" framework of pre-institutions [18]. Two compactness results are presented in this paper: a more informative reformulation of the compactness theorem for pre-institution transformations, and a theorem on natural equivalences with an abstract form of the first-order pre-institution. These results rely on notions of compact transformation, which are introduced as arrow-oriented generalizations...
Compactness in Metric Spaces
In this article, we mainly formalize in Mizar [2] the equivalence among a few compactness definitions of metric spaces, norm spaces, and the real line. In the first section, we formalized general topological properties of metric spaces. We discussed openness and closedness of subsets in metric spaces in terms of convergence of element sequences. In the second section, we firstly formalize the definition of sequentially compact, and then discuss the equivalence of compactness, countable compactness,...
Compactness of Powers of ω
We characterize exactly the compactness properties of the product of κ copies of the space ω with the discrete topology. The characterization involves uniform ultrafilters, infinitary languages, and the existence of nonstandard elements in elementary extensions. We also have results involving products of possibly uncountable regular cardinals.
Compactness=JEP in any logic
Comparing sets of the Baire space by means of general recursive operators
Comparing alternative definitions of Boolean-valued fuzzy sets
Comparing the closed almost disjointness and dominating numbers
We prove that if there is a dominating family of size ℵ₁, then there are ℵ₁ many compact subsets of whose union is a maximal almost disjoint family of functions that is also maximal with respect to infinite partial functions.
Comparing the succinctness of monadic query languages over finite trees
We study the succinctness of monadic second-order logic and a variety of monadic fixed point logics on trees. All these languages are known to have the same expressive power on trees, but some can express the same queries much more succinctly than others. For example, we show that, under some complexity theoretic assumption, monadic second-order logic is non-elementarily more succinct than monadic least fixed point logic, which in turn is non-elementarily more succinct than monadic datalog. Succinctness...
Comparing the succinctness of monadic query languages over finite trees
We study the succinctness of monadic second-order logic and a variety of monadic fixed point logics on trees. All these languages are known to have the same expressive power on trees, but some can express the same queries much more succinctly than others. For example, we show that, under some complexity theoretic assumption, monadic second-order logic is non-elementarily more succinct than monadic least fixed point logic, which in turn is non-elementarily more succinct than monadic datalog. Succinctness...
Comparison game on Borel ideals
We propose and study a “classification” of Borel ideals based on a natural infinite game involving a pair of ideals. The game induces a pre-order and the corresponding equivalence relation. The pre-order is well founded and “almost linear”. We concentrate on and ideals. In particular, we show that all -ideals are -equivalent and form the least equivalence class. There is also a least class of non- Borel ideals, and there are at least two distinct classes of non- ideals.
Comparison of the axioms of local and universal choice
Comparisons between some generalizations of recursion theory
Compatibilité entre conduites sociales réelles dans des groupes et les représentations symboliques de ces groupes : un essai de formalisation mathématique
Compatibility and central elements in pseudo-effect algebras
An equivalent definition of compatibility in pseudo-effect algebras is given, and its relationships with central elements are investigated. Furthermore, pseudo-MV-algebras are characterized among pseudo-effect algebras by means of compatibility.
Compatibility and partial compatibility in quantum logics
Compatible Idempotent Terms in Universal Algebra
In universal algebra, we oftentimes encounter varieties that are not especially well-behaved from any point of view, but are such that all their members have a “well-behaved core”, i.e. subalgebras or quotients with satisfactory properties. Of special interest is the case in which this “core” is a retract determined by an idempotent endomorphism that is uniformly term definable (through a unary term ) in every member of the given variety. Here, we try to give a unified account of this phenomenon....
Complementation in the lattice of Borel structures