Some cardinal characteristics of ordered sets
For ordered (= partially ordered) sets we introduce certain cardinal characteristics of them (some of those are known). We show that these characteristics—with one exception—coincide.
Some remarks on set theory XI
Some Special Properties of Cofinality of Ordinal Numbers.
Sur quelques problèmes arithmétiques de la théorie des nombres ordinaux
The Axiom of Choice, the Löwenheim-Skolem Theorem and Borel models
The Cartesian product of sets and the Hessenberg natural product of ordinals
The product of two ordinals is hereditarily dually discrete
In Dually discrete spaces, Topology Appl. 155 (2008), 1420–1425, Alas et. al. proved that ordinals are hereditarily dually discrete and asked whether the product of two ordinals has the same property. In Products of certain dually discrete spaces, Topology Appl. 156 (2009), 2832–2837, Peng proved a number of partial results and left open the question of whether the product of two stationary subsets of is dually discrete. We answer the first question affirmatively and as a consequence also give...
The Rediscovery of the Cantor-Dedekind Correspondence.
The regularity properties on the real line
The sup = max problem for the extent and the Lindelöf degree of generalized metric spaces, II
In [The sup = max problem for the extent of generalized metric spaces, Comment. Math. Univ. Carolin. The special issue devoted to Čech 54 (2013), no. 2, 245–257], the author and Yajima discussed the sup = max problem for the extent and the Lindelöf degree of generalized metric spaces: (strict) -spaces, (strong) -spaces and semi-stratifiable spaces. In this paper, the sup = max problem for the Lindelöf degree of spaces having -diagonals and for the extent of spaces having point-countable bases...
The sup = max problem for the extent of generalized metric spaces
It looks not useful to study the sup = max problem for extent, because there are simple examples refuting the condition. On the other hand, the sup = max problem for Lindelöf degree does not occur at a glance, because Lindelöf degree is usually defined by not supremum but minimum. Nevertheless, in this paper, we discuss the sup = max problem for the extent of generalized metric spaces by combining the sup = max problem for the Lindelöf degree of these spaces.
Théories des bornes
Tightly packed families of sots
Über Teilsysteme von ...({g}).
Über zwei Bezeichnungssysteme für Ordinalzahlen.
Uncountable cardinals have the same monadic ∀₁¹ positive theory over large sets
We show that uncountable cardinals are indistinguishable by sentences of the monadic second-order language of order of the form (∀X)ϕ(X) and (∃X)ϕ(X), for ϕ positive in X and containing no set-quantifiers, when the set variables range over large (= cofinal) subsets of the cardinals. This strengthens the result of Doner-Mostowski-Tarski [3] that (κ,∈), (λ,∈) are elementarily equivalent when κ, λ are uncountable. It follows that we can consistently postulate that the structures , are indistinguishable...
Walks on countable ordinals and selective ultrafilters
Weakly normal ideals ou PKl and the singular cardinal hypothesis
In §1, we observe that a weakly normal ideal has a saturation property; we also show that the existence of certain precipitous ideals is sufficient for the existence of weakly normal ideals. In §2, generalizing Solovay’s theorem concerning strongly compact cardinals, we show that is decided if carries a weakly normal ideal and λ is regular or cf λ ≤ κ. This is applied to solving the singular cardinal hypothesis.
Вполне замкнутые отображения и совместимость некоторых теорем общей топологии с аксиомами теории множеств
О числе попарно несравнимых порядковых типов.