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Displaying 61 – 80 of 389

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Set-theoretic constructions of two-point sets

Ben Chad, Robin Knight, Rolf Suabedissen (2009)

Fundamenta Mathematicae

A two-point set is a subset of the plane which meets every line in exactly two points. By working in models of set theory other than ZFC, we demonstrate two new constructions of two-point sets. Our first construction shows that in ZFC + CH there exist two-point sets which are contained within the union of a countable collection of concentric circles. Our second construction shows that in certain models of ZF, we can show the existence of two-point sets without explicitly invoking the Axiom of Choice....

Seven characterizations of non-meager 𝖯-filters

Kenneth Kunen, Andrea Medini, Lyubomyr Zdomskyy (2015)

Fundamenta Mathematicae

We give several topological/combinatorial conditions that, for a filter on ω, are equivalent to being a non-meager -filter. In particular, we show that a filter is countable dense homogeneous if and only if it is a non-meager -filter. Here, we identify a filter with a subspace of 2 ω through characteristic functions. Along the way, we generalize to non-meager -filters a result of Miller (1984) about -points, and we employ and give a new proof of results of Marciszewski (1998). We also employ a theorem...

Several results on set-valued possibilistic distributions

Ivan Kramosil, Milan Daniel (2015)

Kybernetika

When proposing and processing uncertainty decision-making algorithms of various kinds and purposes, we more and more often meet probability distributions ascribing non-numerical uncertainty degrees to random events. The reason is that we have to process systems of uncertainties for which the classical conditions like σ -additivity or linear ordering of values are too restrictive to define sufficiently closely the nature of uncertainty we would like to specify and process. In cases of non-numerical...

Currently displaying 61 – 80 of 389