Rolando Jimenez, Viacheslav I. Malykhin (1998)
Commentationes Mathematicae Universitatis Carolinae
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We introduce the general notion of structure resolvability and structure irresolvability, generalizing the usual concepts of resolvability and irresolvability.
Michał Morayne (1992)
Fundamenta Mathematicae
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We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.
Udayan Darji (1993)
Colloquium Mathematicae
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Galvin and Prikry defined completely Ramsey sets and showed that the class of completely Ramsey sets forms a σ-algebra containing open sets. However, they used two definitions of completely Ramsey. We show that they are not equivalent as they remarked. One of these definitions is a more uniform property than the other. We call it the uniformly completely Ramsey property. We show that some of the results of Ellentuck, Silver, Brown and Aniszczyk concerning completely Ramsey sets also...
Miroslav Repický (1991)
Commentationes Mathematicae Universitatis Carolinae
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We shall investigate some properties of forcing which are preserved by finite support iterations and which ensure that unbounded families in given partially ordered sets remain unbounded.
Saharon Shelah (2000)
Fundamenta Mathematicae
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We prove that it is consistent that the covering number of the ideal of measure zero sets has countable cofinality.
Andrzej Nowik (1999)
Colloquium Mathematicae
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We prove some properties of uniformly completely Ramsey null sets (for example, every hereditarily Menger set is uniformly completely Ramsey null).