On invariants for measure preserving transformations
The classification problem for measure preserving transformations is strictly more complicated than that of graph isomorphism.
On isomorphism classes of spaces
We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces , the topological sums of Cantor cubes , with smaller than the first sequential cardinal, and intervals of ordinal numbers [0,α]. In particular, we prove that it is relatively consistent with ZFC that the only isomorphism classes of spaces with ≥ ℵ₀ and α ≥ ω₁ are the trivial ones. This result leads to some elementary questions on large cardinals.
On isomorphisms between -ideals on
On iterated forcing for successors of regular cardinals
We investigate the problem of when ≤λ-support iterations of < λ-complete notions of forcing preserve λ⁺. We isolate a property- properness over diamonds-that implies λ⁺ is preserved and show that this property is preserved by λ-support iterations. Our condition is a relative of that presented by Rosłanowski and Shelah in [2]; it is not clear if the two conditions are equivalent. We close with an application of our technology by presenting a consistency result on uniformizing colorings of ladder...
On Krull's intersection theorem of fuzzy ideals.
On -fuzzy ideals in semirings. I
In this paper we extend the concept of an -fuzzy (characteristic) left (resp. right) ideal of a ring to a semiring , and we show that each level left (resp. right) ideal of an -fuzzy left (resp. right) ideal of is characteristic iff is -fuzzy characteristic.
On -fuzzy ideals in semirings. II
We study some properties of -fuzzy left (right) ideals of a semiring related to level left (right) ideals.
On level by level equivalence and inequivalence between strong compactness and supercompactness
We prove two theorems, one concerning level by level inequivalence between strong compactness and supercompactness, and one concerning level by level equivalence between strong compactness and supercompactness. We first show that in a universe containing a supercompact cardinal but of restricted size, it is possible to control precisely the difference between the degree of strong compactness and supercompactness that any measurable cardinal exhibits. We then show that in an unrestricted size universe...
On Luzin spaces
On (m, n)-ramifications or (m, n)-pseudo-trees of sets.
On Marczewski sets and some ideals.
On Marczewski-Burstin representable algebras
We construct algebras of sets which are not MB-representable. The existence of such algebras was previously known under additional set-theoretic assumptions. On the other hand, we prove that every Boolean algebra is isomorphic to an MB-representable algebra of sets.
On matrix rapid filters
Galois-Tukey equivalence between matrix summability and absolute convergence of series is shown and an alternative characterization of rapid ultrafilters on ω is derived.
On Meager Additive and Null Additive Sets in the Cantor Space and in ℝ
Let T be the standard Cantor-Lebesgue function that maps the Cantor space onto the unit interval ⟨0,1⟩. We prove within ZFC that for every , X is meager additive in iff T(X) is meager additive in ⟨0,1⟩. As a consequence, we deduce that the cartesian product of meager additive sets in ℝ remains meager additive in ℝ × ℝ. In this note, we also study the relationship between null additive sets in and ℝ.
On mean value in -quantum spaces
The paper deals with a new mathematical model for quantum mechanics based on the fuzzy set theory [1]. The indefinite integral of observables is defined and some basic properties of the integral are examined.
On Measurability of Uncountable Unions of Measurable Sets
On metric σ-discrete spaces
By studying dimensional types of metric scattered spaces, we consider the wider class of metric σ-discrete spaces. Applying techniques relevant to this wider class, we present new proofs of some embeddable properties of countable metric spaces in such a way that they can be generalized onto uncountable metric scattered spaces. Related topics are also explored, which gives a few new results.
On Michálek's fuzzy topological spaces
The aim of this paper is to study some properties of Michálek’s fuzzy topology which are quite different of the classic properties of the Chang’s topology.
On minimal separating Boolean algebras.
On models in the alternative set theory