Displaying similar documents to “A dichotomy for P-ideals of countable sets”

On what I do not understand (and have something to say): Part I

Saharon Shelah (2000)

Fundamenta Mathematicae

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This is a non-standard paper, containing some problems in set theory I have in various degrees been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me, sometimes the problems are presented with a discussion of how I have tried to solve them, and sometimes with failed tries, anecdotes and opinions. So the discussion is quite personal, in other words, egocentric and somewhat accidental. As we discuss many problems, history...

Countably metacompact spaces in the constructible universe

Paul Szeptycki (1993)

Fundamenta Mathematicae

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We present a construction from ♢* of a first countable, regular, countably metacompact space with a closed discrete subspace that is not a G δ . In addition some nonperfect spaces with σ-disjoint bases are constructed.

Lindelöf property and the iterated continuous function spaces

G. Sokolov (1993)

Fundamenta Mathematicae

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We give an example of a compact space X whose iterated continuous function spaces C p ( X ) , C p C p ( X ) , . . . are Lindelöf, but X is not a Corson compactum. This solves a problem of Gul’ko (Problem 1052 in [11]). We also provide a theorem concerning the Lindelöf property in the function spaces C p ( X ) on compact scattered spaces with the ω 1 th derived set empty, improving some earlier results of Pol [12] in this direction.

Finite union of H-sets and countable compact sets

Sylvain Kahane (1993)

Colloquium Mathematicae

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In [2], D. E. Grow and M. Insall construct a countable compact set which is not the union of two H-sets. We make precise this result in two directions, proving such a set may be, but need not be, a finite union of H-sets. Descriptive set theory tools like Cantor-Bendixson ranks are used; they are developed in the book of A. S. Kechris and A. Louveau [6]. Two proofs are presented; the first one is elementary while the second one is more general and useful. Using the last one I prove in...

More topological cardinal inequalities

O. Alas (1993)

Colloquium Mathematicae

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A new topological cardinal invariant is defined; it may be considered as a weaker form of the Lindelöf degree.

Very small sets

Haim Judah, Amiran Lior, Ireneusz Recław (1997)

Colloquium Mathematicae

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Representing free Boolean algebras

Alan Dow, P. Nyikos (1992)

Fundamenta Mathematicae

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Partitioner algebras are defined in [2] and are natural tools for studying the properties of maximal almost disjoint families of subsets of ω. In this paper we investigate which free algebras can be represented as partitioner algebras or as subalgebras of partitioner algebras. In so doing we answer a question raised in [2] by showing that the free algebra with ℵ 1 generators is represented. It was shown in [2] that it is consistent that the free Boolean algebra of size continuum is not...

Counting partial types in simple theories

Olivier Lessmann (2000)

Colloquium Mathematicae

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We continue the work of Shelah and Casanovas on the cardinality of families of pairwise inconsistent types in simple theories. We prove that, in a simple theory, there are at most λ < κ ( T ) + 2 μ + | T | pairwise inconsistent types of size μ over a set of size λ. This bound improves the previous bounds and clarifies the role of κ(T). We also compute exactly the maximal cardinality of such families for countable, simple theories. The main tool is the fact that, in simple theories, the collection of nonforking...