On c-sets and products of ideals

Marek Balcerzak

Displaying similar documents to “On c-sets and products of ideals”

Generalized projections of Borel and analytic sets

Marek Balcerzak (1996)

Colloquium Mathematicae

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For a σ-ideal I of sets in a Polish space X and for A ⊆ $X^{2}$ , we consider the generalized projection (A) of A given by (A) = x ∈ X: Ax ∉ I, where $A_{x}$ =y ∈ X: 〈x,y〉∈ A. We study the behaviour of with respect to Borel and analytic sets in the case when I is a $\sum_{2}^{0}$ -supported σ-ideal. In particular, we give an alternative proof of the recent result of Kechris showing that [ $\sum_{1}^{1} (X^{2})] = \sum_{1}^{1} (X)$ for a wide class of $\sum_{2}^{0}$ -supported σ-ideals.

Very small sets

Haim Judah, Amiran Lior, Ireneusz Recław (1997)

Colloquium Mathematicae

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Mycielski ideals generated by uncountable systems

A. Rosłanowski (1993)

Colloquium Mathematicae

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On the maximal spectrum of commutative semiprimitive rings

K. Samei (2000)

Colloquium Mathematicae

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The space of maximal ideals is studied on semiprimitive rings and reduced rings, and the relation between topological properties of Max(R) and algebric properties of the ring R are investigated. The socle of semiprimitive rings is characterized homologically, and it is shown that the socle is a direct sum of its localizations with respect to isolated maximal ideals. We observe that the Goldie dimension of a semiprimitive ring R is equal to the Suslin number of Max(R).