Displaying similar documents to “The σ-ideal of closed smooth sets does not have the covering property”

Borel extensions of Baire measures

J. Aldaz (1997)

Fundamenta Mathematicae

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We show that in a countably metacompact space, if a Baire measure admits a Borel extension, then it admits a regular Borel extension. We also prove that under the special axiom ♣ there is a Dowker space which is quasi-Mařík but not Mařík, answering a question of H. Ohta and K. Tamano, and under P(c), that there is a Mařík Dowker space, answering a question of W. Adamski. We answer further questions of H. Ohta and K. Tamano by showing that the union of a Mařík space and a compact space...

Gaps in analytic quotients

Stevo Todorčević (1998)

Fundamenta Mathematicae

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We prove that the quotient algebra P(ℕ)/I over any analytic ideal I on ℕ contains a Hausdorff gap.

Examples of non-shy sets

Randall Dougherty (1994)

Fundamenta Mathematicae

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Christensen has defined a generalization of the property of being of Haar measure zero to subsets of (abelian) Polish groups which need not be locally compact; a recent paper of Hunt, Sauer, and Yorke defines the same property for Borel subsets of linear spaces, and gives a number of examples and applications. The latter authors use the term “shyness” for this property, and “prevalence” for the complementary property. In the present paper, we construct a number of examples of non-shy...

The measure algebra does not always embed

Alan Dow, Klaas Hart (2000)

Fundamenta Mathematicae

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The Open Colouring Axiom implies that the measure algebra cannot be embedded into P(ℕ)/fin. We also discuss errors in previous results on the embeddability of the measure algebra.

On regular interstices and selective types in countable arithmetically saturated models of Peano Arithmetic

Teresa Bigorajska, Henryk Kotlarski, James Schmerl (1998)

Fundamenta Mathematicae

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We continue the earlier research of [1]. In particular, we work out a class of regular interstices and show that selective types are realized in regular interstices. We also show that, contrary to the situation above definable elements, the stabilizer of an element inside M(0) whose type is selective need not be maximal.

ℳ-rank and meager groups

Ludomir Newelski (1996)

Fundamenta Mathematicae

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Assume p* is a meager type in a superstable theory T. We investigate definability properties of p*-closure. We prove that if T has < 2 ℵ 0 countable models then the multiplicity rank ℳ of every type p is finite. We improve Saffe’s conjecture.

On a question of Sierpiński

Theodore Slaman (1999)

Fundamenta Mathematicae

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There is a set U of reals such that for every analytic set A there is a continuous function f which maps U bijectively to A.