Properties of forcing preserved by finite support iterations
We shall investigate some properties of forcing which are preserved by finite support iterations and which ensure that unbounded families in given partially ordered sets remain unbounded.
Properties of fuzzy relations powers
Properties of - compositions of fuzzy relations were first examined in Goguen [8] and next discussed by many authors. Power sequence of fuzzy relations was mainly considered in the case of matrices of fuzzy relation on a finite set. We consider - powers of fuzzy relations under diverse assumptions about operation. At first, we remind fundamental properties of - composition. Then, we introduce some manipulations on relation powers. Next, the closure and interior of fuzzy relations are examined....
Properties of measure and category in generalized Cohen's and Silver's forcing
Properties of quantum logic maps as fuzzy relations on a set of all symmetric and idempotent binary matrices
A quantum logic is one of possible mathematical models for non-compatible random events. In this work we solve a problem proposed at the conference FSTA 2006. Namely, it is proved that s-maps are symmetric fuzzy relations on a set of all symmetric and idempotent binary matrices. Consequently s-maps are not antisymmetric fuzzy relations. This paper also explores other properties of s-maps, j-maps and d-maps. Specifically, it is proved that s-maps are neither reflexive, nor irreflexive, and nor transitive,...
Properties of the class of measure separable compact spaces
We investigate properties of the class of compact spaces on which every regular Borel measure is separable. This class will be referred to as MS. We discuss some closure properties of MS, and show that some simply defined compact spaces, such as compact ordered spaces or compact scattered spaces, are in MS. Most of the basic theory for regular measures is true just in ZFC. On the other hand, the existence of a compact ordered scattered space which carries a non-separable (non-regular) Borel measure...
Properties of the nearest parametric form approximation operator of fuzzy numbers.
Property C'', strong measure zero sets and subsets of the plane
Let X be a set of reals. We show that • X has property C" of Rothberger iff for all closed F ⊆ ℝ × ℝ with vertical sections (x ∈ X) null, is null; • X has strong measure zero iff for all closed F ⊆ ℝ × ℝ with all vertical sections (x ∈ ℝ) null, is null.
Propositional extensions of [Book]
Propriété de Baire de muni d’une nouvelle topologie et application à la construction d’ultrafiltres
Propriété de Nikodym et propriété de Grothendieck
Propriétés des classes d’éléments -standard
Proto-metrizable fuzzy topological spaces
In this paper we define for fuzzy topological spaces a notion corresponding to proto-metrizable topological spaces. We obtain some properties of these fuzzy topological spaces, particularly we give relations with non-archimedean, and metrizable fuzzy topological spaces.
Provability in the alternative set theory
Provident sets and rudimentary set forcing
Using the theory of rudimentary recursion and provident sets expounded in [MB], we give a treatment of set forcing appropriate for working over models of a theory PROVI which may plausibly claim to be the weakest set theory supporting a smooth theory of set forcing, and of which the minimal model is Jensen’s . Much of the development is rudimentary or at worst given by rudimentary recursions with parameter the notion of forcing under consideration. Our development eschews the power set axiom. We...
P-sets and minimal right ideals in ℕ*
Recall that a P-set is a closed set X such that the intersection of countably many neighborhoods of X is again a neighborhood of X. We show that if 𝔱 = 𝔠 then there is a minimal right ideal of (βℕ,+) that is also a P-set. We also show that the existence of such P-sets implies the existence of P-points; in particular, it is consistent with ZFC that no minimal right ideal is a P-set. As an application of these results, we prove that it is both consistent with and independent of ZFC that the shift...
Pseudodimension of relational structures
Quasi-bounded trees and analytic inductions
A tree T on ω is said to be cofinal if for every there is some branch β of T such that α ≤ β, and quasi-bounded otherwise. We prove that the set of quasi-bounded trees is a complete Σ¹₁-inductive set. In particular, it is neither analytic nor co-analytic.
Quasicoincidence for intuitionistic fuzzy points.
Quasi-minimal posets and lattices.
Quasi-regular Relations – A New Class of Relations on Sets