Αll -dense sets of reals can be isomorphic
α-Properness and Axiom A
We show that under ZFC, for every indecomposable ordinal α < ω₁, there exists a poset which is β-proper for every β < α but not α-proper. It is also shown that a poset is forcing equivalent to a poset satisfying Axiom A if and only if it is α-proper for every α < ω₁.
-structures
-tautologies, uniform and non-uniform upper bounds in computation theory
Una -tautologia è una tautologia del tipo avente un solo interpolante di Craig , a meno di equivalenza logica. Utilizzando misure di complessità relative al problema di trovare tale , mostriamo come si possano ottenere limiti non uniformi di complessità mediante limiti uniformi, e viceversa.
Δ₁-Definability of the non-stationary ideal at successor cardinals
Assuming V = L, for every successor cardinal κ we construct a GCH and cardinal preserving forcing poset ℙ ∈ L such that in the ideal of all non-stationary subsets of κ is Δ₁-definable over H(κ⁺).
Δ-extension and Hanf-numbers
-principal numberings.
ε-partitions and α-equivalences.
The aim of this paper is to study a special type of fuzzy relations, the α-equivalences, as well as to consider the relation that connects these with the family of ε-partitions of the referential. Some classic equivalences between set, partitions and fuzzy relations are also studied.
-satisfiability, -consistency property, the downward Lowenheim Skolem theorem, and the failure of the interpolation theorem for with a strong limit cardinal of cofinality
- Théorie des ensembles
-ideals in the lattice of semi -ideals
-Hamiltonian and -regular algebraic structures
The concept of a -closed subset was introduced in [1] for an algebraic structure of type and a set of open formulas of the first order language . The set of all -closed subsets of forms a complete lattice whose properties were investigated in [1] and [2]. An algebraic structure is called - hamiltonian, if every non-empty -closed subset of is a class (block) of some congruence on ; is called - regular, if for every two , whenever they have a congruence class in common....
-cofinalities of
-porosity is separably determined
We prove a separable reduction theorem for -porosity of Suslin sets. In particular, if is a Suslin subset in a Banach space , then each separable subspace of can be enlarged to a separable subspace such that is -porous in if and only if is -porous in . Such a result is proved for several types of -porosity. The proof is done using the method of elementary submodels, hence the results can be combined with other separable reduction theorems. As an application we extend a theorem...
-допустимые семейства над линейными порядками.
-предикаты конечных типов над допустимым множеством
σ-Entangled linear orders and narrowness of products of Boolean algebras
We investigate σ-entangled linear orders and narrowness of Boolean algebras. We show existence of σ-entangled linear orders in many cardinals, and we build Boolean algebras with neither large chains nor large pies. We study the behavior of these notions in ultraproducts.
σ-ring and σ-algebra of Sets1
In this article, semiring and semialgebra of sets are formalized so as to construct a measure of a given set in the next step. Although a semiring of sets has already been formalized in [13], that is, strictly speaking, a definition of a quasi semiring of sets suggested in the last few decades [15]. We adopt a classical definition of a semiring of sets here to avoid such a confusion. Ring of sets and algebra of sets have been formalized as non empty preboolean set [23] and field of subsets [18],...
-continuity between two pointwise quasi-uniformity spaces.
-categoricity of generalized products